Signal processing apparatus

ABSTRACT

The present disclosure describes a method and an apparatus for analyzing measured signals using various processing techniques. In certain embodiments, the measured signals are physiological signals. In certain embodiments, the measurements relate to blood constituent measurements including blood oxygen saturation.

PRIORITY CLAIM

This application is a continuation of U.S. patent application Ser. No.12/410,422 (Atty. Dock. No. MASIMO.7CP1C21C), filed Mar. 24, 2009, whichis a continuation of U.S. patent application Ser. No. 11/842,117 (Atty.Dock. No. MASIMO.7CP1C21), filed Aug. 20, 2007 (now U.S. Pat. No.7,509,154), which is a continuation of U.S. patent application Ser. No.09/195,791 (Atty. Dock. No. MASIMO.7CP1C5), filed Nov. 17, 1998 (nowU.S. Pat. No. 7,328,053), which is a continuation of U.S. patentapplication Ser. No. 08/859,837 (Atty. Dock. No. MASIMO.7CP1C1), filedMay 16, 1997 (now U.S. Pat. No. 6,157,850), which is a continuation ofU.S. patent application Ser. No. 08/320,154 (Atty. Dock. No.MASIMO.7CP1), filed Oct. 7, 1994 (now U.S. Pat. No. 5,632,272), each ofwhich is incorporated by reference herein in its entirety.

REFERENCE TO RELATED APPLICATIONS

The present application is related to at least the following U.S.utility applications:

Filing App. Sr. No. Date Title Atty Dock. 1 11/894,716 Aug. 20, SIGNALMASIMO.7CP1C20 2007 PROCESSING APPARATUS 2 11/766,714 Jun. 21, SIGNALMASIMO.7CP1C19 2007 PROCESSING APPARATUS 3 11/754,238 May 25, SIGNALMASIMO.7CP1C18 2007 PROCESSING APPARATUS 4 11/766,719 Jun. 21, SIGNALMASIMO.7CP1C17 2007 PROCESSING APPARATUS 5 11/766,700 Jun. 21, SIGNALMASIMO.7CP1C16 2007 PROCESSING APPARATUS 6 11/432,278 May 11, SIGNALMASIMO.7CP1C15 2006 PROCESSING APPARATUS 7 11/070,081 Mar. 2, SIGNALMASIMO.7CP1C13 2005 PROCESSING APPARATUS 8 11/003,231 Dec. 3, SIGNALMASIMO.7CP1C12 2004 PROCESSING APPARATUS 9 10/838,814 May 4, SIGNALMASIMO.7CP1C9D1 2004 PROCESSING APPARATUS 10 10/676,534 Sep. 30, SIGNALMASIMO.7CP1C11 2003 PROCESSING APPARATUS 11 10/677,050 Sep. 30, SIGNALMASIMO.7CP1C10 2003 PROCESSING APPARATUS 12 09/195,791 Nov. 17, SIGNALMASIMO.7CP1C5 1998 PROCESSING APPARATUS 13 09/144,897 Sep. 1, SIGNALMASIMO.7CP1C4 1998 PROCESSING APPARATUS 14 09/110,542 Jul. 6, SIGNALMASIMO.7CP1C3 1998 PROCESSING APPARATUS

The present application incorporates the foregoing disclosures herein byreference in their entirety.

FIELD OF THE INVENTION

The present invention relates to the field of signal processing. Morespecifically, the present invention relates to the processing ofmeasured signals, containing a primary signal portion and a secondarysignal portion, for the removal or derivation of either the primary orsecondary signal portion when little is known about either of thesecomponents. More particularly, the present invention relates to modelingthe measured signals in a novel way which facilitates minimizing thecorrelation between the primary signal portion and the secondary signalportion in order to produce a primary and/or secondary signal. Thepresent invention is especially useful for physiological monitoringsystems including blood oxygen saturation systems.

BACKGROUND OF THE INVENTION

Signal processors are typically employed to remove or derive either theprimary or secondary signal portion from a composite measured signalincluding a primary signal portion and a secondary signal portion. Forexample, a composite signal may contain noise and desirable portions. Ifthe secondary signal portion occupies a different frequency spectrumthan the primary signal portion, then conventional filtering techniquessuch as low pass, band pass, and high pass filtering are available toremove or derive either the primary or the secondary signal portion fromthe total signal. Fixed single or multiple notch filters could also beemployed if the primary and/or secondary signal portion(s) exist at afixed frequency(s).

It is often the case that an overlap in frequency spectrum between theprimary and secondary signal portions exists. Complicating mattersfurther, the statistical properties of one or both of the primary andsecondary signal portions change with time. In such cases, conventionalfiltering techniques are ineffective in extracting either the primary orsecondary signal. If, however, a description of either the primary orsecondary signal portion can be derived, correlation canceling, such asadaptive noise canceling, can be employed to remove either the primaryor secondary signal portion of the signal isolating the other portion.In other words, given sufficient information about one of the signalportions, that signal portion can be extracted.

Conventional correlation cancelers, such as adaptive noise cancelers,dynamically change their transfer function to adapt to and removeportions of a composite signal. However, correlation cancelers requireeither a secondary reference or a primary reference which correlates toeither the secondary signal portion only or the primary signal portiononly. For instance, for a measured signal containing noise and desirablesignal, the noise can be removed with a correlation canceler if a noisereference is available. This is often the case. Although the amplitudeof the reference signals are not necessarily the same as the amplitudeof the corresponding primary or secondary signal portions, they have afrequency spectrum which is similar to that of the primary or secondarysignal portions.

In many cases, nothing or very little is known about the secondaryand/or primary signal portions. One area where measured signalscomprising a primary signal portion and a secondary signal portion aboutwhich no information can easily be determined is physiologicalmonitoring. Physiological monitoring generally involves measured signalsderived from a physiological system, such as the human body.Measurements which are typically taken with physiological monitoringsystems include electrocardiographs, blood pressure, blood gassaturation (such as oxygen saturation), capnographs, other bloodconstituent monitoring, heart rate, respiration rate,electro-encephalograph (EEG) and depth of anesthesia, for example. Othertypes of measurements include those which measure the pressure andquantity of a substance within the body such as cardiac output, venousoxygen saturation, arterial oxygen saturation, bilirubin, totalhemoglobin, breathalyzer testing, drug testing, cholesterol testing,glucose testing, extra vasation, and carbon dioxide testing, proteintesting, carbon monoxide testing, and other in-vivo measurements, forexample. Complications arising in these measurements are often due tomotion of the patient, both external and internal (muscle movement,vessel movement, and probe movement, for example), during themeasurement process.

Many types of physiological measurements can be made by using the knownproperties of energy attenuation as a selected form of energy passesthrough a medium.

A blood gas monitor is one example of a physiological monitoring systemwhich is based upon the measurement of energy attenuated by biologicaltissues or substances. Blood gas monitors transmit light into the testmedium and measure the attenuation of the light as a function of time.The output signal of a blood gas monitor which is sensitive to thearterial blood flow contains a component which is a waveformrepresentative of the patient's arterial pulse. This type of signal,which contains a component related to the patient's pulse, is called aplethysmographic wave, and is shown in FIG. 1 as curve s.Plethysmographic waveforms are used in blood gas saturationmeasurements. As the heart beats, the amount of blood in the arteriesincreases and decreases, causing increases and decreases in energyattenuation, illustrated by the cyclic wave s in FIG. 1.

Typically, a digit such as a finger, an ear lobe, or other portion ofthe body where blood flows close to the skin, is employed as the mediumthrough which light energy is transmitted for blood gas attenuationmeasurements. The finger comprises skin, fat, bone, muscle, etc., shownschematically in FIG. 2, each of which attenuates energy incident on thefinger in a generally predictable and constant manner. However, whenfleshy portions of the finger are compressed erratically, for example bymotion of the finger, energy attenuation becomes erratic.

An example of a more realistic measured waveform S is shown in FIG. 3,illustrating the effect of motion. The primary plethysmographic waveformportion of the signal s is the waveform representative of the pulse,corresponding to the sawtooth-like pattern wave in FIG. 1. The large,secondary motion-induced excursions in signal amplitude obscure theprimary plethysmographic signal s. Even small variations in amplitudemake it difficult to distinguish the primary signal component s in thepresence of a secondary signal component n.

A pulse oximeter is a type of blood gas monitor which non-invasivelymeasures the arterial saturation of oxygen in the blood. The pumping ofthe heart forces freshly oxygenated blood into the arteries causinggreater energy attenuation. As well understood in the art, the arterialsaturation of oxygenated blood may be determined from the depth of thevalleys relative to the peaks of two plethysmographic waveforms measuredat separate wavelengths. Patient movement introduces motion artifacts tothe composite signal as illustrated in the plethysmographic waveformillustrated in FIG. 3. These motion artifacts distort the measuredsignal.

SUMMARY

This invention provides improvements upon the methods and apparatusdisclosed in U.S. patent application Ser. No. 08/132,812, filed Oct. 6,1993, entitled Signal Processing Apparatus, which earlier applicationhas been assigned to the assignee of the instant application. Thepresent invention involves several different embodiments using the novelsignal model in accordance with the present invention to isolate eithera primary signal portion or a secondary signal portion of a compositemeasured signal. In one embodiment, a signal processor acquires a firstmeasured signal and a second measured signal that is correlated to thefirst measured signal. The first signal comprises a first primary signalportion and a first secondary signal portion. The second signalcomprises a second primary signal portion and a second secondary signalportion. The signals may be acquired by propagating energy through amedium and measuring an attenuated signal after transmission orreflection. Alternatively, the signals may be acquired by measuringenergy generated by the medium.

In one embodiment, the first and second measured signals are processedto generate a secondary reference which does not contain the primarysignal portions from either of the first or second measured signals.This secondary reference is correlated to the secondary signal portionof each of the first and second measured signals. The secondaryreference is used to remove the secondary portion of each of the firstand second measured signals via a correlation canceler, such as anadaptive noise canceler. The correlation canceler is a device whichtakes a first and second input and removes from the first input allsignal components which are correlated to the second input. Any unitwhich performs or nearly performs this function is herein considered tobe a correlation canceler.

An adaptive correlation canceler can be described by analogy to adynamic multiple notch filter which dynamically changes its transferfunction in response to a reference signal and the measured signals toremove frequencies from the measured signals that are also present inthe reference signal. Thus, a typical adaptive correlation cancelerreceives the signal from which it is desired to remove a component andreceives a reference signal of the undesired portion. The output of thecorrelation canceler is a good approximation to the desired signal withthe undesired component removed.

Alternatively, the first and second measured signals may be processed togenerate a primary reference which does not contain the secondary signalportions from either of the first or second measured signals. Theprimary reference may then be used to remove the primary portion of eachof the first and second measured signals via a correlation canceler. Theoutput of the correlation canceler is a good approximation to thesecondary signal with the primary signal removed and may be used forsubsequent processing in the same instrument or an auxiliary instrument.In this capacity, the approximation to the secondary signal may be usedas a reference signal for input to a second correlation cancelertogether with either the first or second measured signals forcomputation of, respectively, either the first or second primary signalportions.

Physiological monitors can benefit from signal processors of the presentinvention. Often in physiological measurements a first signal comprisinga first primary portion and a first secondary portion and a secondsignal comprising a second primary portion and a second secondaryportion are acquired. The signals may be acquired by propagating energythrough a patient's body (or a material which is derived from the body,such as breath, blood, or tissue, for example) or inside a vessel andmeasuring an attenuated signal after transmission or reflection.Alternatively, the signal may be acquired by measuring energy generatedby a patient's body, such as in electrocardiography. The signals areprocessed via the signal processor of the present invention to acquireeither a secondary reference or a primary reference which is input to acorrelation canceler, such as an adaptive noise canceler.

One physiological monitoring apparatus which benefits from the presentinvention is a monitoring system which determines a signal which isrepresentative of the arterial pulse, called a plethysmographic wave.This signal can be used in blood pressure calculations, bloodconstituent measurements, etc. A specific example of such a use is inpulse oximetry. Pulse oximetry involves determining the saturation ofoxygen in the blood. In this configuration, the primary portion of thesignal is the arterial blood contribution to attenuation of energy as itpasses through a portion of the body where blood flows close to theskin. The pumping of the heart causes blood flow to increase anddecrease in the arteries in a periodic fashion, causing periodicattenuation wherein the periodic waveform is the plethysmographicwaveform representative of the arterial pulse. The secondary portion isnoise. In accordance with the present invention, the measured signalsare modeled such that this secondary portion of the signal is related tothe venous blood contribution to attenuation of energy as it passesthrough the body. The secondary portion also includes artifacts due topatient movement which causes the venous blood to flow in anunpredictable manner, causing unpredictable attenuation and corruptingthe otherwise periodic plethysmographic waveform. Respiration alsocauses the secondary or noise portion to vary, although typically at alower frequency than the patients pulse rate. Accordingly, the measuredsignal which forms a plethysmographic waveform is modeled in accordancewith the present invention such that the primary portion of the signalis representative of arterial blood contribution to attenuation and thesecondary portion is due to several other parameters.

A physiological monitor particularly adapted to pulse oximetry oxygensaturation measurement comprises two light emitting diodes (LED's) whichemit light at different wavelengths to produce first and second signals.A detector registers the attenuation of the two different energy signalsafter each passes through an absorptive media, for example a digit suchas a finger, or an earlobe. The attenuated signals generally compriseboth primary (arterial attenuator) and secondary (noise) signalportions. A static filtering system, such as a bandpass filter, removesa portion of the secondary signal which is outside of a known bandwidthof interest, leaving an erratic or random secondary signal portion,often caused by motion and often difficult to remove, along with theprimary signal portion.

A processor in accordance with one embodiment of the present inventionremoves the primary signal portions from the measured signals yielding asecondary reference which is a combination of the remaining secondarysignal portions. The secondary reference is correlated to both of thesecondary signal portions. The secondary reference and at least one ofthe measured signals are input to a correlation canceler, such as anadaptive noise canceler, which removes the random or erratic portion ofthe secondary signal. This yields a good approximation to a primaryplethysmographic signal as measured at one of the measured signalwavelengths. As is known in the art, quantitative measurements of theamount of oxygenated arterial blood in the body can be determined fromthe plethysmographic signal in a variety of ways.

The processor of the present invention may also remove the secondarysignal portions from the measured signals yielding a primary referencewhich is a combination of the remaining primary signal portions. Theprimary reference is correlated to both of the primary signal portions.The primary reference and at least one of the measured signals are inputto a correlation canceler which removes the primary portions of themeasured signals. This yields a good approximation to the secondarysignal at one of the measured signal wavelengths. This signal may beuseful for removing secondary signals from an auxiliary instrument aswell as determining venous blood oxygen saturation.

In accordance with the signal model of the present invention, the twomeasured signals each having primary and secondary signal portions canbe related by coefficients. By relating the two equations with respectto coefficients defined in accordance with the present invention, thecoefficients provide information about the arterial oxygen saturationand about the noise (the venous oxygen saturation and other parameters).In accordance with this aspect of the present invention, thecoefficients can be determined by minimizing the correlation between theprimary and secondary signal portions as defined in the model.Accordingly, the signal model of the present invention can be utilizedin many ways in order to obtain information about the measured signalsas will be further apparent in the detailed description of the preferredembodiments.

One aspect of the present invention is a method for use in a signalprocessor in a signal processor for processing at least two measuredsignals S₁ and S₂ each containing a primary signal portion s and asecondary signal portion n, the signals S₁ and S₂ being in accordancewith the following relationship:

S ₁ =s ₁ +n ₁

S ₂ =s ₂ +n ₂

where s₁ and s₂, and n₁ and n₂ are related by:

s ₁ =r _(a) s ₂ and n ₁ =r _(v) n ₂

and where r_(a) and r_(v) are coefficients.

The method comprises a number of steps. A value of coefficient r_(a) isdetermined which minimize correlation between s₁ and n₁. Then, at leastone of the first and second signals is processed using the determinedvalue for r_(a) to significantly reduce n from at least one of the firstor second measured signal to form a clean signal.

In one embodiment, the clean signal is displayed on a display. Inanother embodiment, wherein the first and second signals arephysiological signals, the method further comprises the step ofprocessing the clean signal to determine a physiological parameter fromthe first or second measured signals. In one embodiment, the parameteris arterial oxygen saturation. In another embodiment, the parameter isan ECG signal. In yet another embodiment, wherein the first portion ofthe measured signals is indicative of a heart plethysmograph, the methodfurther comprises the step of calculating the pulse rate.

Another aspect of the present invention involves a physiologicalmonitor. The monitor has a first input configured to receive a firstmeasured signal S₁ having a primary portion, s₁, and a secondary portionn₁. The monitor also has a second input configured to received a secondmeasured signal S₂ having a primary portion s₂ and a secondary portionn₂. Advantageously, the first and the second measured signals S₁ and S₂are in accordance with the following relationship:

S ₁ =s ₁ +n ₁

S ₂ =S ₂ +n ₂

where s₁ and s₂, and n₁ and n₂ are related by:

s ₁ =r _(a) s ₂ and n ₁ =r _(v) n ₂

and where r_(a) and r_(v) are coefficients.

The monitor further has a scan reference processor, the scan referenceprocessor responds to a plurality of possible values for r_(a) tomultiply the second measured signal by each of the possible values forr_(a) and for each of the resulting values, to subtract the resultingvalues from the first measured signal to provide a plurality of outputsignals. A correlation canceler having a first input configured toreceive the first measured signal, and having a second input configuredto receive the plurality of output signals from the saturation scanreference processor, provides a plurality of output vectorscorresponding to the correlation cancellation between the plurality ofoutput signals and the first measured signal. An integrator having aninput configured to receive the plurality of output vectors from thecorrelation canceler is responsive to the plurality of output vectors todetermine a corresponding power for each output vector. An extremumdetector is coupled at its input to the output of the integrator. Theextremum detector is responsive to the corresponding power for eachoutput vector to detect a selected power.

In one embodiment, the plurality of possible values correspond to aplurality of possible values for a selected blood constituent. In oneembodiment the, the selected blood constituent is arterial blood oxygensaturation. In another embodiment, the selected blood constituent isvenous blood oxygen saturation. In yet another embodiment, the selectedblood constituent is carbon monoxide.

Another aspect of the present invention involves a physiologicalmonitor. The monitor has a first input configured to receive a firstmeasured signal S₁ having a primary portion, s₁, and a secondaryportion, n₁. The monitor also has a second input configured to receiveda second measured signal S₂ having a primary portion s₂ and a secondaryportion n₂. The first and the second measured signals S₁ and S₂ are inaccordance with the following relationship:

S ₁ =s ₁ +n ₁

S ₂ =s ₂ +n ₂

where s₁ and s₂, and n₁ and n₂ are related by:

s ₁ =r _(a) s ₂ and n ₁ =r _(v) n _(s)

and where r_(a) and r_(v) are coefficients.

A transform module is responsive to the first and the second measuredsignals and responsive to a plurality of possible values for r_(a) toprovide at least one power curve as an output. An extremum calculationmodule is responsive to the at least one power curve to select a valuefor r_(a) which minimizes the correlation between s and n, and tocalculate from the value for r_(a) a corresponding saturation value asan output. A display module is responsive to the output of saturationcalculation to display the saturation value.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates an ideal plethysmographic waveform.

FIG. 2 schematically illustrates a typical finger.

FIG. 3 illustrates a plethysmographic waveform which includes amotion-induced erratic signal portion.

FIG. 4 a illustrates a schematic diagram of a physiological monitor tocompute primary physiological signals.

FIG. 4 b illustrates a schematic diagram of a physiological monitor tocompute secondary signals.

FIG. 5 a illustrates an example of an adaptive noise canceler whichcould be employed in a physiological monitor, to compute primaryphysiological signals.

FIG. 5 b illustrates an example of an adaptive noise canceler whichcould be employed in a physiological monitor, to compute secondarymotion artifact signals.

FIG. 5 c illustrates the transfer function of a multiple notch filter.

FIG. 6 a illustrates a schematic of absorbing material comprising Nconstituents within the absorbing material.

FIG. 6 b illustrates another schematic of absorbing material comprisingN constituents, including one mixed layer, within the absorbingmaterial.

FIG. 6 c illustrates another schematic of absorbing material comprisingN constituents, including two mixed layers, within the absorbingmaterial.

FIG. 7 a illustrates a schematic diagram of a monitor, to computeprimary and secondary signals in accordance with one aspect of thepresent invention.

FIG. 7 b illustrates the ideal correlation canceler energy or poweroutput as a function of the signal coefficients r₁, r₂, . . . r_(n). Inthis particular example, r₃=r_(a) and r₇=r_(v).

FIG. 7 c illustrates the non-ideal correlation canceler energy or poweroutput as a function of the signal coefficients r₁, r₂, . . . r_(n). Inthis particular example, r₃=r_(a) and r₇=r_(v).

FIG. 8 is a schematic model of a joint process estimator comprising aleast-squares lattice predictor and a regression filter.

FIG. 8 a is a schematic model of a joint process estimator comprising aQRD least-squares lattice (LSL) predictor and a regression filter.

FIG. 9 is a flowchart representing a subroutine for implementing insoftware a joint process estimator as modeled in FIG. 8.

FIG. 9 a is a flowchart representing a subroutine for implementing insoftware a joint process estimator as modeled in FIG. 8 a.

FIG. 10 is a schematic model of a joint process estimator with aleast-squares lattice predictor and two regression filters.

FIG. 10 a is a schematic model of a joint process estimator with a QRDleast-squares lattice predictor and two regression filters.

FIG. 11 is an example of a physiological monitor in accordance with theteachings of one aspect of the present invention.

FIG. 11 a illustrates an example of a low noise emitter current driverwith accompanying digital to analog converter.

FIG. 12 illustrates the front end analog signal conditioning circuitryand the analog to digital conversion circuitry of the physiologicalmonitor of FIG. 11.

FIG. 13 illustrates further detail of the digital signal processingcircuitry of FIG. 11.

FIG. 14 illustrates additional detail of the operations performed by thedigital signal processing circuitry of FIG. 11.

FIG. 15 illustrates additional detail regarding the demodulation moduleof FIG. 14.

FIG. 16 illustrates additional detail regarding the decimation module ofFIG. 14.

FIG. 17 represents a more detailed block diagram of the operations ofthe statistics module of FIG. 14.

FIG. 18 illustrates a block diagram of the operations of one embodimentof the saturation transform module of FIG. 14.

FIG. 19 illustrates a block diagram of the operation of the saturationcalculation module of FIG. 14.

FIG. 20 illustrates a block diagram of the operations of the pulse ratecalculation module of FIG. 14.

FIG. 21 illustrates a block diagram of the operations of the motionartifact suppression module of FIG. 20.

FIG. 21 a illustrates an alternative block diagram for the operations ofthe motion artifact suppression module of FIG. 20.

FIG. 22 illustrates a saturation transform curve in accordance with theprinciples of the present invention.

FIG. 23 illustrates a block diagram of an alternative embodiment to thesaturation transform in order to obtain a saturation value.

FIG. 24 illustrates a histogram saturation transform in accordance withthe alternative embodiment of FIG. 23.

FIGS. 25A-25C illustrate yet another alternative embodiment in order toobtain the saturation.

FIG. 26 illustrates a signal measured at a red wavelength λa=λred=660 nmfor use in a processor of the present invention for determining thesecondary reference n′(t) or the primary reference s′(t) and for use ina correlation canceler. The measured signal comprises a primary portions_(λa)(t) and a secondary portion n_(λa)(t).

FIG. 27 illustrates a signal measured at an infrared wavelengthλb=λ_(IR)=910 nm for use in a processor of the present invention fordetermining the secondary reference n′(t) or the primary reference s′(t)and for use in a correlation canceler. The measured signal comprises aprimary portion s_(λb)(t) and a secondary portion n_(λb)(t).

FIG. 28 illustrates the secondary reference n′(t) determined by aprocessor of the present invention.

FIG. 29 illustrates a good approximation s″_(λa)(t) to the primaryportion s_(λa)(t) of the signal S_(λa)(t) measured at λa=λred=660 nmestimated by correlation cancellation with a secondary reference n′(t).

FIG. 30 illustrates a good approximation s″_(λb)(t) to the primaryportion s_(λb)(t) of the signal S_(λb)(t) measured at λb=λIR=910 nmestimated by correlation cancellation with a secondary reference n′(t).

FIG. 31 depicts a set of 3 concentric electrodes, i.e., a tripolarelectrode sensor, to derive electrocardiography (ECG) signals, denotedas S₁, S₂ and S₃, for use with the present invention. Each of the ECGsignals contains a primary portion and a secondary portion.

DETAILED DESCRIPTION

The present invention involves a system which utilizes first and secondmeasured signals that each contain a primary signal portion and asecondary signal portion. In other words, given a first and secondcomposite signals S₁(t)=s₁(t)+n₁(t) and S₂(t)=s₂(t)+n₂(t), the system ofthe present invention can be used to isolate either the primary signalportion s(t) or the secondary signal portion n(t). Following processing,the output of the system provides a good approximation n″(t) to thesecondary signal portion n(t) or a good approximation s″(t) to theprimary signal portion s(t).

The system of the present invention is particularly useful where theprimary and/or secondary signal portion n(t) may contain one or more ofa constant portion, a predictable portion, an erratic portion, a randomportion, etc. The primary signal approximation s″(t) or secondary signalapproximation n″(t) is derived by removing as many of the secondarysignal portions n(t) or primary signal portions s(t) from the compositesignal S(t) as possible. The remaining signal forms either the primarysignal approximation s″(t) or secondary signal approximation n″(t),respectively. The constant portion and predictable portion of thesecondary signal n(t) are easily removed with traditional filteringtechniques, such as simple subtraction, low pass, band pass, and highpass filtering. The erratic portion is more difficult to remove due toits unpredictable nature. If something is known about the erraticsignal, even statistically, it could be removed, at least partially,from the measured signal via traditional filtering techniques. However,often no information is known about the erratic portion of the secondarysignal n(t). In this case, traditional filtering techniques are usuallyinsufficient.

In order to remove the secondary signal n(t), a signal model inaccordance with the present invention is defined as follows for thefirst and second measured signals S₁ and S₂:

S ₁ =s ₁ +n ₁

S ₂ =s ₂ +n ₂

with

s ₁ =r _(a) s ₂ and n ₁ =r _(v) n ₂

or

$r_{a} = {{\frac{s_{1}}{s_{2}}\mspace{14mu} {and}\mspace{14mu} n_{1}} = \frac{n_{1}}{n_{2}}}$

where s₁ and n₁ are at least somewhat (preferably substantially)uncorrelated and s₂ and n₂ are at least somewhat (preferablysubstantially) uncorrelated. The first and second measured signals S₁and S₂ are related by correlation coefficients r_(a) and r_(v) asdefined above. The use and selection of these coefficients is describedin further detail below.

In accordance with one aspect of the present invention, this signalmodel is used in combination with a correlation canceler, such as anadaptive noise canceler, to remove or derive the erratic portion of themeasured signals.

Generally, a correlation canceler has two signal inputs and one output.One of the inputs is either the secondary reference n′(t) or the primaryreference s′(t) which are correlated, respectively, to the secondarysignal portions n(t) and the primary signal portions s(t) present in thecomposite signal S(t). The other input is for the composite signal S(t).Ideally, the output of the correlation canceler s″(t) or n″(t)corresponds, respectively, to the primary signal s(t) or the secondarysignal n(t) portions only. Often, the most difficult task in theapplication of correlation cancelers is determining the referencesignals n′(t) and s′(t) which are correlated to the secondary n(t) andprimary s(t) portions, respectively, of the measured signal S(t) since,as discussed above, these portions are quite difficult to isolate fromthe measured signal S(t). In the signal processor of the presentinvention, either a secondary reference n′(t) or a primary references′(t) is determined from two composite signals measured simultaneously,or nearly simultaneously, at two different wavelengths, λa and λb.

A block diagram of a generic monitor incorporating a signal processoraccording to the present invention, and a correlation canceler is shownin FIGS. 4 a and 4 b. Two measured signals, S_(λa)(t) and S_(λb)(t), areacquired by a detector 20. One skilled in the art will realize that forsome physiological measurements, more than one detector may beadvantageous. Each signal is conditioned by a signal conditioner 22 aand 22 b. Conditioning includes, but is not limited to, such proceduresas filtering the signals to remove constant portions and amplifying thesignals for ease of manipulation. The signals are then converted todigital data by an analog-to-digital converter 24 a and 24 b. The firstmeasured signal S_(λa)(t) comprises a first primary signal portion,labeled herein s_(λa)(t), and a first secondary signal portion, labeledherein n_(λa)(t). The second measured signal S_(λb)(t) is at leastpartially correlated to the first measured signal S_(λa)(t) andcomprises a second primary signal portion, labeled herein s_(λb)(t), anda second secondary signal portion, labeled herein n_(λb)(t). Typicallythe first and second secondary signal portions, n_(λa)(t) and n_(λb)(t),are uncorrelated and/or erratic with respect to the primary signalportions s_(λa)(t) and s_(λb)(t). The secondary signal portionsn_(λa)(t) and n_(λb)(t) are often caused by motion of a patient inphysiological measurements.

The signals S_(λa)(t) and S_(λb)(t) are input to a reference processor26. The reference processor 26 multiplies the second measured signalS_(λb)(t) by either a factor r_(a)=s_(λa)(t)/s_(λb)(t) or a factorr_(v)=n_(λa)(t)/n_(λb)(t) and then subtracts the second measured signalS_(λb)(t) from the first measured signal S_(λa)(t). The signalcoefficient factors r_(a) and r_(v) are determined to cause either theprimary signal portions s_(λa)(t) and s_(λb)(t) or the secondary signalportions n_(λa)(t) and n_(λb)(t) to cancel, respectively, when the twosignals S_(λa)(t) and S_(λb)(t) are subtracted. Thus, the output of thereference processor 26 is either a secondary reference signaln′(t)=n_(λa)(t)−r_(a)n_(λb)(t), in FIG. 4 a, which is correlated to bothof the secondary signal portions n_(λa)(t) and n_(λb)(t) or a primaryreference signal s′(t)=s_(λa)(t)−r_(v)s_(λb)(t), in FIG. 4 b, which iscorrelated to both of the primary signal portions s_(λa)(t) ands_(λb)(t). A reference signal n′(t) or s′(t) is input, along with one ofthe measured signals S_(λa)(t) or S_(λb)(t), to a correlation canceler27 which uses the reference signal n′(t) or s′(t) to remove either thesecondary signal portions n_(λa)(t) or n_(λb)(t) or the primary signalportions s_(λa)(t) or s_(λb)(t) from the measured signal S_(λa)(t) orS_(λb)(t). The output of the correlation canceler 27 is a good primarysignal approximation s″(t) or secondary signal approximation n″(t). Inone embodiment, the approximation s″(t) or n″(t) is displayed on adisplay 28.

In one embodiment, an adaptive noise canceler 30, an example of which isshown in block diagram form in FIG. 5 a, is employed as the correlationcanceler 27, to remove either one of the erratic, secondary signalportions n_(λa)(t) and n_(λb)(t) from the first and second signalsS_(λa)(t) and S_(λb)(t). The adaptive noise canceler 30 in FIG. 5 a hasas one input a sample of the secondary reference n′(t) which iscorrelated to the secondary signal portions n_(λa)(t) and n_(λb)(t). Thesecondary reference n′(t) is determined from the two measured signalsS_(λa)(t) and S_(λb)(t) by the processor 26 of the present invention asdescribed herein. A second input to the adaptive noise canceler, is asample of either the first or second composite measured signalsS_(λa)(t)=s_(λa)(t)+n_(λa)(t) or S_(λb)(t)=s_(λb)(t)+n_(λb)(t).

The adaptive noise canceler 30, in FIG. 5 b, may also be employed toremove either one of primary signal portions s_(λa)(t) and s_(λb)(t)from the first and second measured signals S_(λa)(t) and S_(λb)(t). Theadaptive noise canceler 30 has as one input a sample of the primaryreference s′(t) which is correlated to the primary signal portionss_(λa)(t) and s_(λb)(t). The primary reference s′(t) is determined fromthe two measured signals S_(λa)(t) and S_(λb)(t) by the processor 26 ofthe present invention as described herein. A second input to theadaptive noise canceler 30 is a sample of either the first or secondmeasured signals S_(λa)(t)=s_(λa)(t)+n_(λa)(t) orS_(λb)(t)=s_(λb)(t)+n_(λb)(t).

The adaptive noise canceler 30 functions to remove frequencies common toboth the reference n′(t) or s′(t) and the measured signal S_(λa)(t) orS_(λb)(t). Since the reference signals are correlated to either thesecondary signal portions n_(λa)(t) and n_(λb)(t) or the primary signalportions s_(λa)(t) and s_(λb)(t), the reference signals will becorrespondingly erratic or well behaved. The adaptive noise canceler 30acts in a manner which may be analogized to a dynamic multiple notchfilter based on the spectral distribution of the reference signal n′(t)or s′(t).

FIG. 5 c illustrates an exemplary transfer function of a multiple notchfilter. The notches, or dips in the amplitude of the transfer function,indicate frequencies which are attenuated or removed when a signalpasses through the notch filter. The output of the notch filter is thecomposite signal having frequencies at which a notch is present removed.In the analogy to an adaptive noise canceler 30, the frequencies atwhich notches are present change continuously based upon the inputs tothe adaptive noise canceler 30.

The adaptive noise canceler 30 (FIGS. 5 a and 5 b) produces an outputsignal, labeled herein as s″_(λa)(t), s″_(λb)(t), n″_(λa)(t) orn″_(λb)(t) which is fed back to an internal processor 32 within theadaptive noise canceler 30. The internal processor 32 automaticallyadjusts its own transfer function according to a predetermined algorithmsuch that the output of the internal processor 32 labeled b_(λ)(t) inFIG. 5 a and c _(λ)(t) in FIG. 5 b, closely resembles either thesecondary signal portion n_(λa)(t) or n_(λb)(t) or the primary signalportion s_(λa)(t) or s_(λb)(t). The output b_(λ)(t) of the internalprocessor 32 in FIG. 5 a is subtracted from the measured signal,S_(λa)(t) or S_(λb)(t), yielding a signal outputs″_(λa)(t)=s_(λa)(t)+n_(λa)(t)−b_(λa)(t) or a signal outputs″_(λb)(t)=s_(λb)(t)+n_(λb)(t)−b_(λb)(t). The internal processoroptimizes s″_(λa)(t) or s″_(λb)(t) such that s″_(λa)(t) or s″_(λb)(t) isapproximately equal to the primary signal s_(λa)(t) or s_(λb)(t),respectively. The output c_(λ)(t) of the internal processor 32 in FIG. 5b is subtracted from the measured signal, S_(λa)(t) or S_(λb)(t),yielding a signal output given byn″_(λa)(t)=s_(λa)(t)+n_(λa)(t)−c_(λa)(t) or a signal output given byn″_(λb)(t)=s_(λb)(t)+n_(λb)(t)−c_(λb)(t). The internal processoroptimizes n″_(λa)(t) or n″_(λb)(t) such that n″_(λa)(t) or n″_(λb)(t) isapproximately equal to the secondary signal portion n_(λa)(t) orn_(λb)(t), respectively.

One algorithm which may be used for the adjustment of the transferfunction of the internal processor 32 is a least-squares algorithm, asdescribed in Chapter 6 and Chapter 12 of the book Adaptive SignalProcessing by Bernard Widrow and Samuel Stearns, published by PrenticeHall, copyright 1985. This entire book, including Chapters 6 and 12, ishereby incorporated herein by reference.

Adaptive processors 30 in FIGS. 5 a and 5 b have been successfullyapplied to a number of problems including antenna sidelobe canceling,pattern recognition, the elimination of periodic interference ingeneral, and the elimination of echoes on long distance telephonetransmission lines. However, considerable ingenuity is often required tofind a suitable reference signal n′(t) or s′(t) since the portionsn_(λa)(t), n_(λb)(t), s_(λa)(t) and s_(λb)(t) cannot easily be separatedfrom the measured composite signals S_(λa)(t) and S_(λb)(t). If eitherthe actual secondary portion n_(λa)(t) or n_(λb)(t) or the primarysignal portion s_(λa)(t) or s_(λb)(t) were a priori available,techniques such as correlation cancellation would not be necessary.

Generalized Determination of Primary and Secondary Reference Signals

An explanation which describes how the reference signals n′(t) and s′(t)may be determined follows. A first signal is measured at, for example, awavelength λ_(a), by a detector yielding a signal S_(λa)(t):

S _(λa)(t)=s _(λa)(t)+n _(λa)(t)

where s_(λa)(t) is the primary signal portion and n_(λa)(t) is thesecondary signal portion.

A similar measurement is taken simultaneously, or nearly simultaneously,at a different wavelength, λb, yielding:

S _(λb)(t)=s _(λb)(t)+n _(λb)(t)

Note that as long as the measurements, S_(λa)(t) and S_(λb)(t), aretaken substantially simultaneously, the secondary signal components,n_(λa)(t) and n_(λb)(t), are correlated because any random or erraticfunctions affect each measurement in nearly the same fashion. Thesubstantially predictable primary signal components, s_(λa)(t) ands_(λb)(t), are also correlated to one another.

To obtain the reference signals n′(t) and s′(t), the measured signalsS_(λa)(t) and S_(λb)(t) are transformed to eliminate, respectively, theprimary or secondary signal components. In accordance with the presentinvention one way of doing this is to find proportionality constants,r_(a) and r_(v), between the primary signal portions s_(λa)(t) ands_(λb)(t) and the secondary signal portions n_(λa)(t) and n_(λb)(t) suchthat the signals can be modeled as follows:

s _(λa)(t)=r _(a) s _(λb)(t)

n _(λa)(t)=r _(v) n _(λb)(t).  (3)

In accordance with the inventive signal model of the present invention,these proportionality relationships can be satisfied in manymeasurements, including but not limited to absorption measurements andphysiological measurements. Additionally, in accordance with the signalmodel of the present invention, in most measurements, theproportionality constants r_(a) and r_(v) can be determined such that:

n _(λa)(t)≠r _(a) n _(λb)(t)

s _(λa)(t)≠r _(v) s _(λb)(t).  (4)

Multiplying equation (2) by r_(a) and then subtracting equation (2) fromequation (1) results in a single equation wherein the primary signalterms s_(λa)(t) and s_(λb)(t) cancel:

n′(t)=S _(λa)(t)−r _(a) S _(λb)(t)=n _(λa)(t)−r _(a) n _(λb)(t);  (5a)

a non-zero signal which is correlated to each secondary signal portionn_(λa)(t) and n_(λb)(t) and can be used as the secondary reference n′(t)in a correlation canceler such as an adaptive noise canceler.

Multiplying equation (2) by r_(v) and then subtracting equation (2) fromequation (1) results in a single equation wherein the secondary signalterms n_(λa)(t) and n_(λb)(t) cancel, leaving:

s′(t)=S _(λa)(t)−r _(v) S _(λb)(t)=s _(λa)(t)−r _(v) s _(λb)(t);  (5b)

a non-zero signal which is correlated to each of the primary signalportions s_(λa)(t) and s_(λb)(t) and can be used as the signal references′(t) in a correlation canceler such as an adaptive noise canceler.

Example of Determination of Primary and Secondary Reference Signals inan Absorptive System

Correlation canceling is particularly useful in a large number ofmeasurements generally described as absorption measurements. An exampleof an absorption type monitor which can advantageously employcorrelation canceling, such as adaptive noise canceling, based upon areference n′(t) or s′(t) determined by a processor of the presentinvention is one which determines the concentration of an energyabsorbing constituent within an absorbing material when the material issubject to change. Such changes can be caused by forces about whichinformation is desired or primary, or alternatively, by random orerratic secondary forces such as a mechanical force on the material.Random or erratic interference, such as motion, generates secondarycomponents in the measured signal. These secondary components can beremoved or derived by the correlation canceler if a suitable secondaryreference n′(t) or primary reference s′(t) is known.

A schematic N constituent absorbing material comprising a container 42having N different absorbing constituents, labeled A₁, A₂, A₃, . . .A_(N), is shown in FIG. 6 a. The constituents A₁ through A_(N) in FIG. 6a are arranged in a generally orderly, layered fashion within thecontainer 42. An example of a particular type of absorptive system isone in which light energy passes through the container 42 and isabsorbed according to the generalized Beer-Lambert Law of lightabsorption. For light of wavelength λa, this attenuation may beapproximated by:

$\begin{matrix}{I = {I_{o}{\exp \left( {{- \sum\limits_{i = 1}^{N}} \in_{i,{\lambda \; a}}{c_{i}x_{i}}} \right)}}} & (6)\end{matrix}$

Initially transforming the signal by taking the natural logarithm ofboth sides and manipulating terms, the signal is transformed such thatthe signal components are combined by addition rather thanmultiplication, i.e.:

$\begin{matrix}{S_{\pi} = {{\ln \left( {I_{o}/I} \right)} = {\sum\limits_{i = 1}^{N}{\in_{i,{\lambda \; a}}{c_{i}x_{i}}}}}} & (7)\end{matrix}$

where I₀ is the incident light energy intensity; I is the transmittedlight energy intensity; ε_(i,λa) is the absorption coefficient of thei^(th) constituent at the wavelength λa; x_(i)(t) is the optical pathlength of i^(th) layer, i.e., the thickness of material of the i^(th)layer through which optical energy passes; and c_(i)(t) is theconcentration of the i^(th) constituent in the volume associated withthe thickness x_(i)(t). The absorption coefficients ε₁ through ε_(N) areknown values which are constant at each wavelength. Most concentrationsc₁(t) through c_(N)(t) are typically unknown, as are most of the opticalpath lengths x_(i)(t) of each layer. The total optical path length isthe sum of each of the individual optical path lengths x_(i)(t) of eachlayer.

When the material is not subject to any forces which cause change in thethicknesses of the layers, the optical path length of each layer,x_(i)(t), is generally constant. This results in generally constantattenuation of the optical energy and thus, a generally constant offsetin the measured signal. Typically, this offset portion of the signal isof little interest since knowledge about a force which perturbs thematerial is usually desired. Any signal portion outside of a knownbandwidth of interest, including the constant undesired signal portionresulting from the generally constant absorption of the constituentswhen not subject to change, is removed. This is easily accomplished bytraditional band pass filtering techniques. However, when the materialis subject to forces, each layer of constituents may be affected by theperturbation differently than other layers. Some perturbations of theoptical path lengths of each layer x_(i)(t) may result in excursions inthe measured signal which represent desired or primary information.Other perturbations of the optical path length of each layer x_(i)(t)cause undesired or secondary excursions which mask primary informationin the measured signal. Secondary signal components associated withsecondary excursions must also be removed to obtain primary informationfrom the measured signal. Similarly, the ability to compute secondarysignal components caused by secondary excursions directly allows one toobtain primary signal components from the measured signal via simplesubtraction, or correlation cancellation techniques.

The correlation canceler may selectively remove from the compositesignal, measured after being transmitted through or reflected from theabsorbing material, either the secondary or the primary signalcomponents caused by forces which perturb or change the materialdifferently from the forces which perturbed or changed the material tocause respectively, either the primary or secondary signal component.For the purposes of illustration, it will be assumed that the portion ofthe measured signal which is deemed to be the primary signal s_(λa)(t)is the attenuation term ε₅c₅x₅(t) associated with a constituent ofinterest, namely A₅, and that the layer of constituent A₅ is affected byperturbations different than each of the layers of other constituents A₁through A₄ and A₆ through A_(N). An example of such a situation is whenlayer A₅ is subject to forces about which information is deemed to beprimary and, additionally, the entire material is subject to forceswhich affect each of the layers. In this case, since the total forceaffecting the layer of constituent A₅ is different than the total forcesaffecting each of the other layers and information is deemed to beprimary about the forces and resultant perturbation of the layer ofconstituent A₅, attenuation terms due to constituents A₁ through A₄ andA₆ through A_(N) make up the secondary signal portion n_(λa)(t). Even ifthe additional forces which affect the entire material cause the sameperturbation in each layer, including the layer of A₅, the total forceson the layer of constituent A₅ cause it to have different totalperturbation than each of the other layers of constituents A₁ through A₄and A₆ through A_(N).

It is often the case that the total perturbation affecting the layersassociated with the secondary signal components is caused by random orerratic forces. This causes the thickness of layers to changeerratically and the optical path length of each layer, x_(i)(t), tochange erratically, thereby producing a random or erratic secondarysignal component n_(λa)(t). However, regardless of whether or not thesecondary signal portion n_(λa)(t) is erratic, the secondary signalcomponent n_(λa)(t) can be either removed or derived via a correlationcanceler, such as an adaptive noise canceler, having as one input,respectively, a secondary reference n′(t) or a primary reference s′(t)determined by a processor of the present invention as long as theperturbation on layers other than the layer of constituent A₅ isdifferent than the perturbation on the layer of constituent A₅. Thecorrelation canceler yields a good approximation to either the primarysignal s_(λa)(t) or the secondary signal n_(λa)(t). In the event that anapproximation to the primary signal is obtained, the concentration ofthe constituent of interest, c₅(t), can often be determined since insome physiological measurements, the thickness of the primary signalcomponent, x₅(t) in this example, is known or can be determined.

The correlation canceler utilizes either the secondary reference n′(t)or the primary reference s′(t) determined from two substantiallysimultaneously measured signals S_(λa)(t) and S_(λb)(t). S_(λa)(t) isdetermined as above in equation (7). S_(λb)(t) is determined similarlyat a different wavelength λb. To find either the secondary referencen′(t) or the primary reference s′(t), attenuated transmitted energy ismeasured at the two different wavelengths λa and λb and transformed vialogarithmic conversion. The signals S_(λa)(t) and S_(λb)(t) can then bewritten (logarithm converted) as:

$\begin{matrix}{{S_{\lambda \; a}(t)} = {\in_{5,{\lambda \; a}}{{c_{5}{x_{5}(t)}} + \sum\limits_{i = 1}^{4}} \in_{i,{\lambda \; a}}{{c_{i}x_{i}} + \sum\limits_{i = 6}^{N}} \in_{i,{\lambda \; a}}{c_{i}x_{i}}}} & (8) \\{S_{\lambda \; {a{(t)}}} = {{ɛ_{5,{\lambda \; a}}c_{5}{x_{5}(t)}} + {n_{\lambda \; a}(t)}}} & (9) \\{S_{\lambda \; {b{(t)}}} = {\in_{5,{\lambda \; b}}{{c_{5}{x_{5}(t)}} + \sum\limits_{i = 1}^{4}} \in_{i,\; {\lambda \; b}}{{c_{i}x_{i}} + \sum\limits_{i = 6}^{N}} \in_{i,{\lambda \; b}}{c_{i}x_{i}}}} & (10) \\{S_{\lambda \; {b{(t)}}} = {{ɛ_{5,{\lambda \; b}}c_{5}{x_{5}(t)}} + {n_{\lambda \; b}(t)}}} & (11)\end{matrix}$

Further transformations of the signals are the proportionalityrelationships in accordance with the signal model of the presentinvention defining r_(a) and r_(v), similar to equation (3), whichallows determination of a noise reference n′(t) and a primary references′(t). These are:

ε_(5,λa) =r _(a)ε_(5,λb)  (12a)

n _(λa) =r _(v) n _(λb)  (12b)

where

n _(λa) ≠r _(a) n _(λb)  (13a)

ε_(5,λa) ≠r _(v)ε_(5,λb)  (13b)

It is often the case that both equations (12) and (13) can besimultaneously satisfied. Multiplying equation (11) by r_(a) andsubtracting the result from equation (9) yields a non-zero secondaryreference which is a linear sum of secondary signal components:

$\begin{matrix}{\mspace{79mu} {{n^{\prime}(t)} = {{{S_{\lambda \; a}(t)} - {r_{a}{S_{\lambda \; b}(t)}}} = {{n_{\lambda \; a}(t)} - {r_{a}{n_{\lambda \; b}(t)}}}}}} & \left( {14a} \right) \\{= {\sum\limits_{i = 1}^{4}{\in_{i,{\lambda \; a}}{{c_{i}{x_{i}(t)}} + \sum\limits_{i + 6}^{N}} \in_{i,\; {\lambda \; a}}{{c_{i}{x_{i}(t)}} - {\sum\limits_{i = 1}^{4}r_{a}}} \in_{i,{\lambda \; b}}{{c_{i}{x_{i}(t)}} + {\sum\limits_{i = 6}^{N}r_{a}}} \in_{i,{\lambda \; b}}{c_{i}{x_{i}(t)}}}}} & \left( {15a} \right) \\{= {{\sum\limits_{i = 1}^{4}{c_{i}{{x_{i}(t)}\left\lbrack {\in_{i,{\lambda \; a}}{- r_{a}} \in_{i,{\lambda \; a}}{- r_{a}} \in_{i,{\lambda \; b}}} \right\rbrack}}} + {\sum\limits_{i = 6}^{N}{c_{i}{{x_{i}(t)}\left\lbrack {\in_{1,{\lambda \; a}}{- r_{a}} \in_{i,{\lambda \; b}}} \right\rbrack}}}}} & \left( {16a} \right)\end{matrix}$

Multiplying equation (11) by r_(v) and subtracting the result fromequation (9) yields a primary reference which is a linear sum of primarysignal components:

$\begin{matrix}{{s^{\prime}(t)} = {{{S_{\lambda \; a}(t)} - {r_{v}{S_{\lambda \; b}(t)}}} = {{s_{\lambda \; a}(t)} - {r_{v}{s_{\lambda \; b}(t)}}}}} & \left( {14b} \right) \\{\mspace{40mu} {= {c_{5}{x_{5}(t)}ɛ_{5,{\lambda \; a}}r_{v}c_{5}{x_{5}(t)}ɛ_{5,{\lambda \; b}}}}} & \left( {15b} \right) \\{\mspace{40mu} {= {c_{5}{{{x_{5}(t)}\left\lbrack {ɛ_{5,{\lambda \; a}} - {r_{v}ɛ_{5,{\lambda \; b}}}} \right\rbrack}.}}}} & \left( {16b} \right)\end{matrix}$

A sample of either the secondary reference n′(t) or the primaryreference s′(t), and a sample of either measured signal S_(λa)(t) orS_(λb)(t), are input to a correlation canceler 27, such as an adaptivenoise canceler 30, an example of which is shown in FIGS. 5 a and 5 b anda preferred example of which is discussed herein under the headingPREFERRED CORRELATION CANCELER USING A JOINT PROCESS ESTIMATORIMPLEMENTATION. The correlation canceler 27 removes either the secondaryportion n_(λa)(t) or n_(λb)(t), or the primary portions, s_(λa)(t) ors_(λb)(t), of the measured signal yielding a good approximation toeither the primary signals s″_(λa)(t)≈ε_(5,λa)c₅x₅(t) ors″_(λb)(t)≈ε_(5,λb)c₅x₅(t) or the secondary signals n″_(λa)(t)≈n_(λa)(t)or n″_(λb)(t)≈n_(λb)(t). In the event that the primary signals areobtained, the concentration c₅(t) may then be determined from theapproximation to the primary signal s″_(λa)(t) or s″_(λb)(t) accordingto:

c ₅(t)≈s″ _(λa)(t)/ε_(5,λa) x ₅(t)  (17a)

or

c ₅(t)≈s″ _(λb)(t)/ε_(5,λb) x ₅(t)  (17b)

As discussed previously, the absorption coefficients are constant ateach wavelength λa and λb and the thickness of the primary signalcomponent, x₅(t) in this example, is often known or can be determined asa function of time, thereby allowing calculation of the concentrationc₅(t) of constituent A₅.

Determination of Concentration or Saturation in a Volume Containing Morethan One Constituent

Referring to FIG. 6 b, another material having N different constituentsarranged in layers is shown. In this material, two constituents A₅ andA₆ are found within one layer having thickness x_(5,6)(t)=x₅(t)+x₆(t),located generally randomly within the layer. This is analogous tocombining the layers of constituents A₅ and A₆ in FIG. 6 a. Acombination of layers, such as the combination of layers of constituentsA₅ and A₆, is feasible when the two layers are under the same totalforces which result in the same change of the optical path lengths x₅(t)and x₆(t) of the layers.

Often it is desirable to find the concentration or the saturation, i.e.,a percent concentration, of one constituent within a given thicknesswhich contains more than one constituent and is subject to uniqueforces. A determination of the concentration or the saturation of aconstituent within a given volume may be made with any number ofconstituents in the volume subject to the same total forces andtherefore under the same perturbation or change. To determine thesaturation of one constituent in a volume comprising many constituents,as many measured signals as there are constituents which absorb incidentlight energy are necessary. It will be understood that constituentswhich do not absorb light energy are not consequential in thedetermination of saturation. To determine the concentration, as manysignals as there are constituents which absorb incident light energy arenecessary as well as information about the sum of concentrations.

It is often the case that a thickness under unique motion contains onlytwo constituents. For example, it may be desirable to know theconcentration or saturation of A₅ within a given volume which containsA₅ and A₆. In this case, the primary signals s_(λa)(t) and s_(λb)(t)comprise terms related to both A₅ and A₆ so that a determination of theconcentration or saturation of A₅ or A₆ in the volume may be made. Adetermination of saturation is discussed herein. It will be understoodthat the concentration of A₅ in a volume containing both A₅ and A₆ couldalso be determined if it is known that A₅+A₆=1, i.e., that there are noconstituents in the volume which do not absorb incident light energy atthe particular measurement wavelengths chosen. The measured signalsS_(λa)(t) and S_(λb)(t) can be written (logarithm converted) as:

$\begin{matrix}{{S_{\lambda \; a}(t)} = {{ɛ_{5,{\lambda \; a}}c_{5}{x_{5,6}(t)}} + {ɛ_{6,{\lambda \; a}}c_{6}{x_{5,6}(t)}} + {n_{\lambda \; a}(t)}}} & \left( {18a} \right) \\{\mspace{59mu} {= {{s_{\lambda \; a}(t)} + {n_{\lambda \; a}(t)}}}} & \left( {18b} \right) \\{{S_{\lambda \; b}(t)} = {{ɛ_{5,{\lambda \; b}}c_{5}{x_{5,6}(t)}} + {ɛ_{6,{\lambda \; b}}c_{6}{x_{5,6}(t)}} + {n_{\lambda \; b}(t)}}} & \left( {19a} \right) \\{\mspace{59mu} {= {{s_{\lambda \; b}(t)} + {{n_{\lambda \; b}(t)}.}}}} & \left( {19b} \right)\end{matrix}$

It is also often the case that there may be two or more thicknesseswithin a medium each containing the same two constituents but eachexperiencing a separate motion as in FIG. 6 c. For example, it may bedesirable to know the concentration or saturation of A₅ within a givenvolume which contains A₅ and A₆ as well as the concentration orsaturation of A₃ within a given volume which contains A₃ and A₄, A₃ andA₄ having the same constituency as A₅ and A₆ respectively. In this case,the primary signals s_(λa)(t) and s_(λb)(t) again comprise terms relatedto both A₅ and A₆ and portions of the secondary signals n_(λa)(t) andn_(λb)(t) comprise terms related to both A₃ and A₄. The layers, A₃ andA₄, do not enter into the primary equation because they are assumed tobe perturbed by a different frequency, or random or erratic secondaryforces which are uncorrelated with the primary force. Since constituents3 and 5 as well as constituents 4 and 6 are taken to be the same, theyhave the same absorption coefficients (i.e., ε_(3,λa)=ε_(5,λa);ε_(3,λb)=ε_(5,λb); ε_(4,λa)=ε_(6,λa) and ε_(4,λb)=ε_(6,λb). Generallyspeaking, however, A₃ and A₄ will have different concentrations than A₅and A₆ and will therefore have a different saturation. Consequently asingle constituent within a medium may have one or more saturationsassociated with it. The primary and secondary signals according to thismodel may be written as:

$\begin{matrix}{{s_{\lambda \; a}(t)} = {\left\lbrack {{ɛ_{5,{\lambda \; a}}c_{5}} + {ɛ_{6,{\lambda \; a}}c_{6}}} \right\rbrack {x_{5,6}(t)}}} & \left( {20a} \right) \\{{n_{\lambda \; a}(t)} = {{\left\lbrack {{ɛ_{5,{\lambda \; a}}c_{3}} + {ɛ_{6,{\lambda \; a}}c_{4}}} \right\rbrack {x_{3,4}(t)}} +}} & \; \\{\sum\limits_{i = 1}^{2}{\in_{i,{\lambda \; a}}{{c_{i}{x_{i}(t)}} + \sum\limits_{i = 7}^{n}} \in_{i,{\lambda \; a}}{c_{i}{x_{i}(t)}}}} & \left( {20b} \right) \\{{n_{\lambda \; a}(t)} = {{\left\lbrack {{ɛ_{5,{\lambda \; a}}c_{3}} + {ɛ_{6,{\lambda \; a}}c_{4}}} \right\rbrack {x_{3,4}(t)}} + {n_{\lambda \; a}(t)}}} & \left( {20c} \right) \\{{s_{\lambda \; b}(t)} = {\left\lbrack {{ɛ_{5,{\lambda \; b}}c_{5}} + {ɛ_{6,{\lambda \; b}}c_{6}}} \right\rbrack {x_{5,6}(t)}}} & \left( {21a} \right) \\{{n_{\lambda \; b}(t)} = {{\left\lbrack {{ɛ_{5,{\lambda \; b}}c_{3}} + {ɛ_{6,{\lambda \; b}}c_{4}}} \right\rbrack {x_{3,4}(t)}} +}} & \; \\{\sum\limits_{i = 1}^{2}{\in_{i,{\lambda \; b}}{{c_{i}{x_{i}(t)}} + \sum\limits_{i = 7}^{N}} \in_{i,{\lambda \; b}}{c_{i}{{x_{i}(t)}.}}}} & \left( {21b} \right) \\{{n_{\lambda \; b}(t)} = {{\left\lbrack {{ɛ_{5,{\lambda \; b}}c_{3}} + {ɛ_{6,{\lambda \; b}}c_{4}}} \right\rbrack {x_{3,4}(t)}} + {n_{\lambda \; b}(t)}}} & \left( {21c} \right)\end{matrix}$

where signals n_(λa)(t) and n_(λb)(t) are similar to the secondarysignals n_(λa)(t) and n_(λb)(t) except for the omission of the 3, 4layer.

Any signal portions whether primary or secondary, outside of a knownbandwidth of interest, including the constant undesired secondary signalportion resulting from the generally constant absorption of theconstituents when not under perturbation, should be removed to determinean approximation to either the primary signal or the secondary signalwithin the bandwidth of interest. This is easily accomplished bytraditional band pass filtering techniques. As in the previous example,it is often the case that the total perturbation or change affecting thelayers associated with the secondary signal components is caused byrandom or erratic forces, causing the thickness of each layer, or theoptical path length of each layer, x_(i)(t), to change erratically,producing a random or erratic secondary signal component n_(λa)(t).Regardless of whether or not the secondary signal portion n_(λa)(t) iserratic, the secondary signal component n_(λa)(t) can be removed orderived via a correlation canceler, such as an adaptive noise canceler,having as one input a secondary reference n′(t) or a primary references′(t) determined by a processor of the present invention as long as theperturbation in layers other than the layer of constituents A₅ and A₆ isdifferent than the perturbation in the layer of constituents A₅ and A₆.Either the erratic secondary signal components n_(λa)(t) and n_(λb)(t)or the primary components s_(λa)(t) and s_(λb)(t) may advantageously beremoved from equations (18) and (19), or alternatively equations (20)and (21), by a correlation canceler. The correlation canceler, again,requires a sample of either the primary reference s′(t) or the secondaryreference n′(t) and a sample of either of the composite signalsS_(λa)(t) or S_(λb)(t) of equations (18) and (19).

Determination of Primary and Secondary Reference Signals for SaturationMeasurements

One method for determining reference signals s′(t) or n′(t) from themeasured signals S_(λa)(t) and S_(λb)(t) in accordance with one aspectof the invention is what will be referred to as the constant saturationapproach. In this approach, it is assumed that the saturation of A₅ inthe volume containing A₅ and A₆ and the saturation of A₃ in the volumecontaining A₃ and A₄ remains relatively constant over some period oftime, i.e.:

Saturation(A ₅(t))=c ₅(t)/[c ₅(t)+c ₆(t)]  (22a)

Saturation(A ₃(t))=c ₃(t)/[c ₃(t)+c ₄(t)]  (22b)

Saturation(A ₅(t))={1+[c ₆(t)/c ₅(t)]}⁻¹  (23a)

Saturation(A ₃(t))={1+[c ₄(t)/c ₃(t)]}⁻¹  (23b)

are substantially constant over many samples of the measured signalsS_(λa) and S_(λb). This assumption is accurate over many samples sincesaturation generally changes relatively slowly in physiological systems.

The constant saturation assumption is equivalent to assuming that:

c ₅(t)/c ₆(t)=constant₁  (24a)

c ₃(t)/c ₄(t)=constant₂  (24b)

since the only other term in equations (23a) and (23b) is a constant,namely the numeral 1.

Using this assumption, the proportionality constants r_(a) and r_(v)which allow determination of the secondary reference signal n′(t) andthe primary reference signal s′(t) in the constant saturation methodare:

$\begin{matrix}\begin{matrix}{r_{a} = \frac{{ɛ_{5,{\lambda \; a}}c_{5 -}{x_{5,6}(t)}} + {ɛ_{6,{\lambda \; a}}c_{6}{x_{5,6}(t)}}}{{ɛ_{5,{\lambda \; b}}c_{5}{x_{5,6}(t)}} + {ɛ_{6,{\lambda \; b}}c_{6}{x_{5,6}(t)}}}} \\{= {\frac{s_{\lambda \; a}(t)}{s_{\lambda \; b}(t)}\left( {26a} \right)}} \\{= {\frac{{ɛ_{5,{\lambda \; a}}c_{5}} + {ɛ_{6,{\lambda \; a}}c_{6}}}{{ɛ_{5,{\lambda \; b}}c_{5}} + {ɛ_{6,{\lambda \; b}}c_{6}}}\left( {27a} \right)}} \\{= {\frac{{ɛ_{5,{\lambda \; a}}\left( {c_{5}/c_{6}} \right)} + ɛ_{6,{\lambda \; a}}}{{ɛ_{5,{\lambda \; b}}\left( {c_{5}/c_{6}} \right)} + ɛ_{6,{\lambda \; b}}}\left( {28a} \right)}} \\{\approx {\frac{s_{\lambda \; a}^{''}(t)}{s_{\lambda \; b}^{''}(t)}\left( {29a} \right)}} \\{{= {constant}_{3}};}\end{matrix} & \left( {25a} \right)\end{matrix}$

where

n _(λa)(t)≠r _(a)(t)n _(λb)(t)  (30a)

and

$\begin{matrix}\begin{matrix}{r_{v} = \frac{{ɛ_{5,{\lambda \; a}}c_{3}{x_{3,4}(t)}} + {ɛ_{6,{\lambda \; a}}c_{4}{x_{3,4}(t)}}}{\left. {{ɛ_{5,{\lambda \; b}}c_{3}{x_{3,4}(t)}} + {ɛ_{6,{\lambda \; b}}c_{4}{x_{3,4}(t)}}} \right)}} \\{= {\frac{n_{\lambda \; a}(t)}{n_{\lambda \; b}(t)}\left( {26b} \right)}} \\{= {\frac{{ɛ_{5,{\lambda \; a}}c_{3}} + {ɛ_{6,{\lambda \; a}}c_{4}}}{{ɛ_{5,{\lambda \; b}}c_{3}} + {ɛ_{6,{\lambda \; b}}c_{4}}}\left( {27b} \right)}} \\{= {\frac{{ɛ_{5,{\lambda \; a}}\left( {c_{3}/c_{4}} \right)} + ɛ_{6,{\lambda \; a}}}{{ɛ_{5,{\lambda \; b}}\left( {c_{3}/c_{4}} \right)} + ɛ_{6,{\lambda \; b}}}\left( {28b} \right)}} \\{\approx {\frac{n_{\lambda \; a}^{''}(t)}{n_{\lambda \; b}^{''}(t)}\left( {29b} \right)}} \\{{= {constant}_{4}};}\end{matrix} & \left( {25b} \right)\end{matrix}$

where

s _(λa)(t)≠r _(v)(t)s _(λb)(t).  (30b)

In accordance with the present invention, it is often the case that bothequations (26) and (30) can be simultaneously satisfied to determine theproportionality constants r_(a) and r_(v). Additionally, the absorptioncoefficients at each wavelength ε_(5,λa), ε_(6,λa), ε_(5,λb), andε_(6,λb) are constant and the central assumption of the constantsaturation method is that c₅(t)/c₆(t) and c₃(t)/c₄(t) are constant overmany sample periods. Thus, new proportionality constants r_(a) and r_(v)may be determined every few samples from new approximations to eitherthe primary or secondary signal as output from the correlation canceler.Thus, the approximations to either the primary signals s_(λa)(t) ands_(λb)(t) or the secondary signals n_(λa)(t) and n_(λb)(t), found by thecorrelation canceler for a substantially immediately preceding set ofsamples of the measured signals S_(λa)(t) and S_(λb)(t) are used in aprocessor of the present invention for calculating the proportionalityconstants, r_(a) and r_(v), for the next set of samples of the measuredsignals S_(λa)(t) and S_(λb)(t).

Multiplying equation (19) by r_(a) and subtracting the resultingequation from equation (18) yields a non-zero secondary referencesignal:

n′(t)=S _(λa)(t)−r _(a) S _(λb)(t)=n _(λa)(t)−r _(a) n _(λb)(t).  (31a)

Multiplying equation (19) by r_(v) and subtracting the resultingequation from equation (18) yields a non-zero primary reference signal:

s′(t)=S _(λa)(t)−r _(v) S _(λb)(t)=s _(λa)(t)−r _(v) s _(λb)(t).  (31b)

When using the constant saturation method in patient monitoring, initialproportionality coefficients can be determined as further explainedbelow. It is not necessary for the patient to remain motionless even foran initialization period. With values for the proportionalitycoefficients r_(a) and r_(v) determined, a correlation canceler may beutilized with a secondary reference n′(t) or a primary reference s′(t).

Determination of Signal Coefficients for Primary and Secondary ReferenceSignals Using the Constant Saturation Method

In accordance with one aspect of the present invention, the referenceprocessor 26 of FIGS. 4 a and FIG. 4 b of the present invention may beconfigured to multiply the second measured assumed signalS_(λb)(t)=s_(λb)(t)+n_(λb)(t) by each of a plurality of signalcoefficients r₁, r₂, . . . r_(n) and then subtract each result from thefirst measured signal S_(λa)(t)=s_(λa)(t)+n_(λa)(t) to obtain aplurality of reference signals

R′(r,t)=s _(λa)(t)−rs _(λb)(t)+n _(λa)(t)−rn _(λb)(t)  (32)

for r=r₁, r₂, . . . r_(n) as shown in FIG. 7 a. In other words, aplurality of signal coefficients are chosen to represent a cross sectionof possible signal coefficients.

In order to determine either the primary reference s′(t) or thesecondary reference n′(t) from the above plurality of reference signalsof equation (32), signal coefficients r_(a) and r_(v) are determinedfrom the plurality of assumed signal coefficients r₁, r₂, . . . r_(n).The coefficients r_(a) and r_(v) are selected such that they causeeither the primary signal portions s_(λa)(t) and s_(λb)(t) or thesecondary signal portions n_(λa)(t) and n_(λb)(t) to cancel or nearlycancel when they are substituted into the reference function R′(r, t),e.g.

s _(λa)(t)=r _(a) s _(λb)(t)  (33a)

n _(λa)(t)=r _(v) n _(λb)(t)  (33b)

n′(t)=R′(r _(a) ,t)=n _(λa)(t)−r _(a) n _(λb)(t)  (33c)

s′(t)=R′(r _(v) ,t)=s _(λa)(t)−r _(v) s _(λb)(t).  (33d)

In other words, coefficients r_(a) and r_(v) are selected at valueswhich reflect the minimum of correlation between the primary signalportions and the secondary signal portions. In practice, one does notusually have significant prior information about either the primarysignal portions s_(λa)(t) and s_(λb)(t) or the secondary signal portionsn_(λa)(t) and n_(λb)(t) of the measured signals S_(λa)(t) and S_(λb)(t).The lack of this information makes it difficult to determine which ofthe plurality of coefficients r₁, r₂, . . . r_(n) correspond to thesignal coefficients r_(a)=s_(λa)(t)/s_(λb)(t) andr_(v)=n_(λa)(t)/n_(λb)(t).

One approach to determine the signal coefficients r_(a) and r_(v) fromthe plurality of coefficients r₁, r₂, . . . r_(n) employs the use of acorrelation canceler 27, such as an adaptive noise canceler, which takesa first input which corresponds to one of the measured signals S_(λa)(t)or S_(λb)(t) and takes a second input which corresponds to successivelyeach one of the plurality of reference signals R′(r₁, t), R′(r₂, t), . .. , R′(r_(n), t) as shown in FIG. 7 a. For each of the reference signalsR′(r₁, t), R′(r₂, t), . . . , R′(r_(n), t) the corresponding output ofthe correlation canceler 27 is input to a “squares” operation 28 whichsquares the output of the correlation canceler 27. The output of thesquares operation 28 is provided to an integrator 29 for forming acumulative output signal (a summation of the squares). The cumulativeoutput signal is subsequently input to an extremum detector 31. Thepurpose of the extremum detector 31 is to chose signal coefficientsr_(a) and r_(v) from the set r₁, r₂, . . . r_(n) by observing whichprovide a maximum in the cumulative output signal as in FIGS. 7 b and 7c. In other words, coefficients which provide a maximum integratedoutput, such as energy or power, from the correlation canceler 27correspond to the signal coefficients r_(a) and r_(v) which relate to aminimum correlation between the primary signal portions and thesecondary signal portions in accordance with the signal model of thepresent invention. One could also configure a system geometry whichwould require one to locate the coefficients from the set r₁, r₂, . . .r_(n) which provide a minimum or inflection in the cumulative outputsignal to identify the signal coefficients r_(a) and r_(v).

Use of a plurality of coefficients in the processor of the presentinvention in conjunction with a correlation canceler 27 to determine thesignal coefficients r_(a) and r_(v) may be demonstrated by using theproperties of correlation cancellation. If x, y and z are taken to beany collection of three time varying signals, then the properties ofsome correlation cancelers C(x, y) may be defined as follows:

Property (1) C(x,y)=0 for x,y correlated  (34a)

Property (2) C(x,y)=x for x,y uncorrelated  (34b)

Property (3) C(x+y,z)=C(x,z)+C(y,z)  (34c)

With properties (1), (2) and (3) it is easy to demonstrate that theenergy or power output of a correlation canceler with a first inputwhich corresponds to one of the measured signals S_(λa)(t) or S_(λb)(t)and a second input which corresponds to successively each one of aplurality of reference signals R′(r₁, t), R′(r₂, t), . . . , R′(r_(n),t) can determine the signal coefficients r_(a) and r_(v) needed toproduce the primary reference s′(t) and secondary reference n′(t). If wetake as a first input to the correlation canceler the measured signalS_(λa)(t) and as a second input the plurality of reference signalsR′(r₁, t), R′(r₂, t), . . . , R′(r_(n), t) then the outputs of thecorrelation canceler C(S_(λa)(t), R′(r_(j),t)) for j=1, 2, . . . , n maybe written as

C(s _(λa)(t)+n _(λa)(t),s _(λa)(t)−r _(j) s _(λb)(t)+n _(λa)(t)−r _(j) n_(λb)(t))  (35)

where j=1, 2, . . . , n and we have used the expressions

R′(r,t)=S _(λa)(t)−rS _(λb)(t)  (36)

S _(λa)(t)=s _(λa)(t)+n _(λa)(t)  (37a)

S _(λb)(t)=S _(λb)(t)+n _(λb)(t).  (37b)

The use of property (3) allows one to expand equation (35) into twoterms

C(S _(λa)(t),R′(r,t))=C(s _(λa)(t),s _(λa)(t)−rs _(λb)(t)+n _(λa)(t)−rn_(λb)(t))+C(n _(λa)(t),s _(λa)(t)−rs _(λb)(t)+n _(λa)(t)−rn_(λb)(t))  (38)

so that upon use of properties (1) and (2) the correlation canceleroutput is given by

C(S _(λa)(t),R′(r _(j) ,t))=s _(λa)(t)δ(r _(j) −r _(a))+n _(λa)(t)δ(r_(j) −r _(v))  (39)

where δ (x) is the unit impulse function

δ(x)=0 if x≠0

δ(x)=1 if x=0.  (40)

The time variable, t, of the correlation canceler output C(S_(λa)(t),R′(r_(j), t)) may be eliminated by computing its energy or power. Theenergy of the correlation canceler output is given by

$\begin{matrix}\begin{matrix}{{E_{\lambda \; a}\left( r_{j} \right)} = {\int{C^{2}\left( {{S_{\lambda \; a}(t)},{{R^{\prime}\left( {r_{j},t} \right)}{t}}} \right.}}} \\{= {{{\delta \left( {r_{j} - r_{a}} \right)}{\int{{s_{\lambda \; a}^{2}(t)}{t}}}} + {{\delta \left( {r_{j} - r_{v}} \right)}{\int{{n_{\lambda \; a}^{2}(t)}{{t}.}}}}}}\end{matrix} & \left( {41a} \right)\end{matrix}$

It should be understood that one could, equally well, have chosen themeasured signal S_(λb)(t) as the first input to the correlation cancelerand the plurality of reference signals R′(r₁, t), R′(r₂, t), . . . ,R′(r_(n), t) as the second input. In this event, the correlationcanceler energy output is

$\begin{matrix}\begin{matrix}{{E_{\lambda \; b}\left( r_{j} \right)} = {\int{C^{2}\left( {{S_{\lambda \; b}(t)},{{R^{\prime}\left( {r,t} \right)}{t}}} \right.}}} \\{= {{{\delta \left( {r_{j} - r_{a}} \right)}{\int{{s_{\lambda \; b}^{2}(t)}{t}}}} + {{\delta \left( {r_{j} - r_{v}} \right)}{\int{{n_{\lambda \; b}^{2}(t)}{{t}.}}}}}}\end{matrix} & \left( {41b} \right)\end{matrix}$

It should also be understood that in practical situations the use ofdiscrete time measurement signals may be employed as well as continuoustime measurement signals. A system which performs a discrete transform(e.g., a saturation transform in the present example) in accordance withthe present invention is described with reference to FIGS. 11-22. In theevent that discrete time measurement signals are used, integrationapproximation methods such as the trapezoid rule, midpoint rule, Tick'srule, Simpson's approximation or other techniques may be used to computethe correlation canceler energy or power output. In the discrete timemeasurement signal case, the energy output of the correlation cancelermay be written, using the trapezoid rule, as

$\begin{matrix}{{E_{\lambda \; a}\left( r_{j} \right)} = {{{\delta \left( {r_{j} - r_{a}} \right)}\Delta \; t\left\{ {{\sum\limits_{i = 0}^{n}{s_{\lambda \; a}^{2}\left( t_{i\;} \right)}} - {0.5\left( {{s_{\lambda \; a}^{2}\left( t_{0} \right)} + {s_{\lambda \; a}^{2}\left( t_{n} \right)}} \right)}} \right\}} + {{\delta \left( {r_{j} - r_{v}} \right)}\Delta \; t\left\{ {{\sum\limits_{i = 0}^{n}{n_{\lambda \; a}^{2}\left( t_{i\;} \right)}} - {0.5\left( {{n_{\lambda \; a}^{2}\left( t_{0} \right)} + {n_{\lambda \; a}^{2}\left( t_{n} \right)}} \right)}} \right\}}}} & \left( {42a} \right) \\{{E_{\lambda \; b}(r)} = {{{\delta \left( {r_{j} - r_{a}} \right)}\Delta \; t\left\{ {{\sum\limits_{i = 0}^{n}{s_{\lambda \; b}^{2}\left( t_{i\;} \right)}} - {0.5\left( {{s_{\lambda \; b}^{2}\left( t_{0} \right)} + {s_{\lambda \; b}^{2}\left( t_{n} \right)}} \right)}} \right\}} + {{\delta \left( {r_{j} - r_{v}} \right)}\Delta \; t\left\{ {{\sum\limits_{i = 0}^{n}{n_{\lambda \; b}^{2}\left( t_{i\;} \right)}} - {0.5\left( {{n_{\lambda \; b}^{2}\left( t_{0} \right)} + {n_{\lambda \; b}^{2}\left( t_{n} \right)}} \right)}} \right\}}}} & \left( {42b} \right)\end{matrix}$

where t_(i) is the i^(th) discrete time, t₀ is the initial time, t_(n)is the final time and Δt is the time between discrete time measurementsamples.

The energy functions given above, and shown in FIG. 7 b, indicate thatthe correlation canceler output is usually zero due to correlationbetween the measured signal S_(λa)(t) or S_(λb)(t) and many of theplurality of reference signals R′(r₁, t), R′(r₂, t), . . . , R′(r_(n),t). However, the energy functions are non zero at values of r_(j) whichcorrespond to cancellation of either the primary signal portionss_(λa)(t) and s_(λb)(t) or the secondary signal portions n_(λa)(t) andn_(λb)(t) in the reference signal R′(r_(j), t). These values correspondto the signal coefficients r_(a) and r_(v).

It should be understood that there may be instances in time when eitherthe primary signal portions s_(λa)(t) and s_(λb)(t) or the secondarysignal portions n_(λa)(t) and n_(λb)(t) are identically zero or nearlyzero. In these cases, only one signal coefficient value will providemaximum energy or power output of the correlation canceler.

Since there may be more than one signal coefficient value which providesmaximum correlation canceler energy or power output, an ambiguity mayarise. It may not be immediately obvious which signal coefficienttogether with the reference function R′(r, t) provides either theprimary or secondary reference. In such cases, it is necessary toconsider the constraints of the physical system at hand. For example, inpulse oximetry, it is known that arterial blood, whose signature is theprimary plethysmographic wave, has greater oxygen saturation than venousblood, whose signature is the secondary erratic or random signal.Consequently, in pulse oximetry, the ratio of the primary signals due toarterial pulsation r_(a)=s_(λa)(t)/s_(λb)(t) is the smaller of the twosignal coefficient values while the ratio of the secondary signals dueto mainly venous blood dynamics r_(v)=n_(λa)(t)/n_(λb)(t) is the largerof the two signal coefficient values, assuming λa=660 nm and λb=910 nm.

It should also be understood that in practical implementations of theplurality of reference signals and cross correlator technique, the idealfeatures listed as properties (1), (2) and (3) above will not beprecisely satisfied but will be approximations thereof. Therefore, inpractical implementations of this embodiment of the present invention,the correlation canceler energy curves depicted in FIG. 7 b will notconsist of infinitely narrow delta functions but will have finite widthassociated with them as depicted in FIG. 7 c.

It should also be understood that it is possible to have more than twosignal coefficient values which produce maximum energy or power outputfrom a correlation canceler. This situation arises when the measuredsignals each contain more than two components each of which are relatedby a ratio as follows:

$\begin{matrix}{{{s_{\lambda \; a}(t)} = {\sum\limits_{i = 0}^{n}{f_{{\lambda \; a},i}(t)}}}{{s_{\lambda \; b}(t)} = {\sum\limits_{i = 0}^{n}{f_{{\lambda \; b},i}(t)}}}} & (43)\end{matrix}$

where

f _(λa,i)(t)=r _(i) f _(λb,i)(t) i=1, . . . , n

r _(i) ≠r _(j).

Thus, reference signal techniques together with a correlationcancellation, such as an adaptive noise canceler, can be employed todecompose a signal into two or more signal components each of which isrelated by a ratio.

Preferred Correlation Canceler Using a Joint Process EstimatorImplementation

Once either the secondary reference n′(t) or the primary reference s′(t)is determined by the processor of the present invention, the correlationcanceler can be implemented in either hardware or software. Thepreferred implementation of a correlation canceler is that of anadaptive noise canceler using a joint process estimator.

The least mean squares (LMS) implementation of the internal processor 32described above in conjunction with the adaptive noise canceler of FIGS.5 a and FIG. 5 b is relatively easy to implement, but lacks the speed ofadaptation desirable for most physiological monitoring applications ofthe present invention. Thus, a faster approach for adaptive noisecanceling, called a least-squares lattice joint process estimator model,is used in one embodiment. A joint process estimator 60 is showndiagrammatically in FIG. 8 and is described in detail in Chapter 9 ofAdaptive Filter Theory by Simon Haykin, published by Prentice-Hall,copyright 1986. This entire book, including Chapter 9, is herebyincorporated herein by reference.

The function of the joint process estimator is to remove either thesecondary signal portions n_(λa)(t) or n_(λb)(t) or the primary signalportions s_(λa)(t) or s_(λb)(t) from the measured signals S_(λa)(t) orS_(λb)(t), yielding either a primary signal approximation s″_(λa)(t) ors″_(λb)(t) or a secondary signal approximation n″_(λa)(t) or n″_(λb)(t).Thus, the joint process estimator estimates either the value of theprimary signals s_(λa)(t) or s_(λb)(t) or the secondary signalsn_(λa)(t) or n_(λb)(t). The inputs to the joint process estimator 60 areeither the secondary reference n′(t) or the primary reference s′(t) andthe composite measured signal S_(λa)(t) or S_(λb)(t). The output is agood approximation to the signal S_(λa)(t) or S_(λb)(t) with either thesecondary signal or the primary signal removed, i.e. a goodapproximation to either s_(λa)(t), s_(λb)(t), n_(λa)(t) or n_(λb)(t).

The joint process estimator 60 of FIG. 8 utilizes, in conjunction, aleast square lattice predictor 70 and a regression filter 80. Either thesecondary reference n′(t) or the primary reference s′(t) is input to theleast square lattice predictor 70 while the measured signal S_(λa)(t) orS_(λb)(t) is input to the regression filter 80. For simplicity in thefollowing description, S_(λa)(t) will be the measured signal from whicheither the primary portion s_(λa)(t) or the secondary portion n_(λa)(t)will be estimated by the joint process estimator 60. However, it will benoted that S_(λb)(t) could also be input to the regression filter 80 andthe primary portion s_(λb)(t) or the secondary portion n_(λb)(t) of thissignal could be estimated.

The joint process estimator 60 removes all frequencies that are presentin both the reference n′(t) or s′(t), and the measured signal S_(λa)(t).The secondary signal portion n_(λa)(t) usually comprises frequenciesunrelated to those of the primary signal portion s_(λa)(t). It isimprobable that the secondary signal portion n_(λa)(t) would be ofexactly the same spectral content as the primary signal portions_(λa)(t). However, in the unlikely event that the spectral content ofs_(λa)(t) and n_(λa)(t) are similar, this approach will not yieldaccurate results. Functionally, the joint process estimator 60 comparesthe reference input signal n′(t) or s′(t), which is correlated to eitherthe secondary signal portion n_(λa)(t) or the primary signal portions_(λa)(t), and input signal S_(λa)(t) and removes all frequencies whichare identical. Thus, the joint process estimator 60 acts as a dynamicmultiple notch filter to remove those frequencies in the secondarysignal component n_(λa)(t) as they change erratically with the motion ofthe patient or those frequencies in the primary signal components_(λa)(t) as they change with the arterial pulsation of the patient.This yields a signal having substantially the same spectral content andamplitude as either the primary signal s_(λa)(t) or the secondary signaln_(λa)(t). Thus, the output s″_(λa)(t) or n″_(λa)(t) of the jointprocess estimator 60 is a very good approximation to either the primarysignal s_(λa)(t) or the secondary signal n_(λa)(t).

The joint process estimator 60 can be divided into stages, beginningwith a zero-stage and terminating in an m^(th)-stage, as shown in FIG.8. Each stage, except for the zero-stage, is identical to every otherstage. The zero-stage is an input stage for the joint process estimator60. The first stage through the m^(th)-stage work on the signal producedin the immediately previous stage, i.e., the (m−1)^(th)-stage, such thata good primary signal approximation s″_(λa)(t) or secondary signalapproximation n″_(λa)(t) is produced as output from the m^(th)-stage.

The least-squares lattice predictor 70 comprises registers 90 and 92,summing elements 100 and 102, and delay elements 110. The registers 90and 92 contain multiplicative values of a forward reflection coefficientΓ_(f,m)(t) and a backward reflection coefficient Γ_(b,m)(t) whichmultiply the reference signal n′(t) or s′(t) and signals derived fromthe reference signal n′(t) or s′(t). Each stage of the least-squareslattice predictor outputs a forward prediction error f_(m)(t) and abackward prediction error b_(m)(t). The subscript m is indicative of thestage.

For each set of samples, i.e. one sample of the reference signal n′(t)or s′(t) derived substantially simultaneously with one sample of themeasured signal S_(λa)(t), the sample of the reference signal n′(t) ors′(t) is input to the least-squares lattice predictor 70. The zero-stageforward prediction error f₀(t) and the zero-stage backward predictionerror b₀(t) are set equal to the reference signal n′(t) or s′(t). Thebackward prediction error b₀(t) is delayed by one sample period by thedelay element 110 in the first stage of the least-squares latticepredictor 70. Thus, the immediately previous value of the referencen′(t) or s′(t) is used in calculations involving the first-stage delayelement 110. The zero-stage forward prediction error is added to thenegative of the delayed zero-stage backward prediction error b₀(t−1)multiplied by the forward reflection coefficient value Γ_(f,1)(t)register 90 value, to produce a first-stage forward prediction errorf₁(t). Additionally, the zero-stage forward prediction error f₀(t) ismultiplied by the backward reflection coefficient Γ_(b,1)(t) register 92value and added to the delayed zero-stage backward prediction errorb₀(t−1) to produce a first-stage backward prediction error b₁(t). Ineach subsequent stage, m, of the least square lattice predictor 70, theprevious forward and backward prediction error values, f_(m−1)(t) andb_(m−1)(t−1), the backward prediction error being delayed by one sampleperiod, are used to produce values of the forward and backwardprediction errors for the present stage, f_(m)(t) and b_(m)(t).

The backward prediction error b_(m)(t) is fed to the concurrent stage,m, of the regression filter 80. There it is input to a register 96,which contains a multiplicative regression coefficient valueκ_(m,λa)(t). For example, in the zero-stage of the regression filter 80,the zero-stage backward prediction error b₀(t) is multiplied by thezero-stage regression coefficient κ_(0,λa)(t) register 96 value andsubtracted from the measured value of the signal S_(λa)(t) at a summingelement 106 to produce a first stage estimation error signale_(1,λa)(t). The first-stage estimation error signal e_(1,λa)(t) is afirst approximation to either the primary signal or the secondarysignal. This first-stage estimation error signal e_(1,λa)(t) is input tothe first-stage of the regression filter 80. The first-stage backwardprediction error b₁(t), multiplied by the first-stage regressioncoefficient κ_(1,λa)(t) register 96 value is subtracted from thefirst-stage estimation error signal e_(1,λa)(t) to produce thesecond-stage estimation error e_(2,λa)(t). The second-stage estimationerror signal e_(2,λa)(t) is a second, somewhat better approximation toeither the primary signal s_(λa)(t) or the secondary signal n_(λa)(t).

The same processes are repeated in the least-squares lattice predictor70 and the regression filter 80 for each stage until a goodapproximation e_(m,λa)(t), to either the primary signal s_(λa)(t) or thesecondary signal n_(λa)(t) is determined. Each of the signals discussedabove, including the forward prediction error f_(m)(t), the backwardprediction error b_(m)(t), the estimation error signal e_(m,λa)(t), isnecessary to calculate the forward reflection coefficient Γ_(f,m)(t),the backward reflection coefficient Γ_(b,m)(t), and the regressioncoefficient κ_(m,λa)(t) register 90, 92, and 96 values in each stage, m.In addition to the forward prediction error f_(m)(t), the backwardprediction error b_(m)(t), and the estimation error e_(m,λa)(t) signals,a number of intermediate variables, not shown in FIG. 8 but based on thevalues labeled in FIG. 8, are required to calculate the forwardreflection coefficient Γ_(f,m)(t), the backward reflection coefficientΓ_(b,m)(t), and the regression coefficient κ_(m,λa)(t) register 90,92,and 96 values.

Intermediate variables include a weighted sum of the forward predictionerror squares ℑ_(m)(t), a weighted sum of the backward prediction errorsquares β_(m)(t), a scalar parameter Δ_(m)(t), a conversion factorγ_(m)(t), and another scalar parameter ρ_(m,λa)(t). The weighted sum ofthe forward prediction errors ℑ_(m)(t) is defined as:

$\begin{matrix}{{{_{m}(t)} = {\sum\limits_{i = 1}^{t}{\lambda^{t - i}{{f_{m}(i)}}^{2}}}};} & (44)\end{matrix}$

where λ without a wavelength identifier, a or b, is a constantmultiplicative value unrelated to wavelength and is typically less thanor equal to one, i.e., λ≦1. The weighted sum of the backward predictionerrors β_(m)(t) is defined as:

$\begin{matrix}{{\beta_{m}(t)} = {\sum\limits_{i = 1}^{t}{\lambda^{t = i}{{b_{m}(i)}}^{2}}}} & (45)\end{matrix}$

where, again, λ without a wavelength identifier, a or b, is a constantmultiplicative value unrelated to wavelength and is typically less thanor equal to one, i.e., λ≦1. These weighted sum intermediate errorsignals can be manipulated such that they are more easily solved for, asdescribed in Chapter 9, §9.3 of the Haykin book referenced above anddefined hereinafter in equations (59) and (60).

Description of the Joint Process Estimator

The operation of the joint process estimator 60 is as follows. When thejoint process estimator 60 is turned on, the initial values ofintermediate variables and signals including the parameter Δ_(m−1)(t),the weighted sum of the forward prediction error signals ℑ_(m−1)(t), theweighted sum of the backward prediction error signals β_(m−1)(t), theparameter ρ_(m,λa)(t), and the zero-stage estimation error e_(0,λa)(t)are initialized, some to zero and some to a small positive number δ:

Δ_(m−1)(0)=0;  (46)

ℑ^(m-1)(0)=δ;  (47)

β_(m−1)(0)=δ;  (48)

ρ_(m,λa)(0)=0;  (49)

e _(0,λa)(t)=S _(λa)(t) for t≧0.  (50)

After initialization, a simultaneous sample of the measured signalS_(λa)(t) or S_(λb)(t) and either the secondary reference n′(t) or theprimary reference s′(t) are input to the joint process estimator 60, asshown in FIG. 8. The forward and backward prediction error signals f₀(t)and b₀(t), and intermediate variables including the weighted sums of theforward and backward error signals ℑ₀(t) and β₀(t), and the conversionfactor γ₀(t) are calculated for the zero-stage according to:

f ₀(t)=b ₀(t)=n′(t)  (51a)

ℑ₀(t)=β₀(t)=λℑ₀(t−1)+|n′(t)|²  (52a)

γ₀(t−1)=1  (53a)

if a secondary reference n′(t) is used or according to:

f ₀(t)=b ₀(t)=s′(t)  (51b)

ℑ₀(t)=β₀(t)=λℑ₀(t−1)+|s′(t)|²  (52b)

γ₀(t−1)=1  (53b)

if a primary reference s′(t) is used where, again, λ without awavelength identifier, a or b, is a constant multiplicative valueunrelated to wavelength.

Forward reflection coefficient Γ_(f,m)(t), backward reflectioncoefficient Γ_(b,m)(t), and regression coefficient κ_(m,λa)(t) register90, 92 and 96 values in each stage thereafter are set according to theoutput of the previous stage. The forward reflection coefficientΓ_(f,1)(t), backward reflection coefficient Γ_(b,1)(t), and regressioncoefficient κ_(1,λa)(t) register 90, 92 and 96 values in the first stageare thus set according to the algorithm using values in the zero-stageof the joint process estimator 60. In each stage, m≧1, intermediatevalues and register values including the parameter Δ_(m−1)(t); theforward reflection coefficient Γ_(f,m)(t) register 90 value; thebackward reflection coefficient Γ_(b,m)(t) register 92 value; theforward and backward error signals f_(m)(t) and b_(m)(t); the weightedsum of squared forward prediction errors ℑ_(f,m)(t), as manipulated in§9.3 of the Haykin book; the weighted sum of squared backward predictionerrors β_(b,m)(t), as manipulated in §9.3 of the Haykin book; theconversion factor γ_(m)(t); the parameter ρ_(m,λa)(t); the regressioncoefficient κ_(m,λa)(t) register 96 value; and the estimation errore_(m+1λa)(t) value are set according to:

Δ_(m−1)(t)=λΔ_(m−1)(t−1)+{b _(m−1)(t−1)f* _(m−1)(t)/γ_(m−1)(t−1)}  (54)

Γ_(f,m)(t)=−{Δ_(m−1)(t)/β_(m−1)(t−1)}  (55)

Γ_(b,m)(t)=−{Δ*_(m−1)(t)/ℑ_(m−1)(t)}  (56)

f _(m)(t)=f _(m−1)(t)+Γ*_(f,m)(t)b _(m−1)(t−1)  (57)

b _(m)(t)=b _(m−1)(t−1)+Γ*_(b,m)(t)f _(m−1)(t)  (58)

ℑ_(m)(t)=ℑ_(m−1)(t)−{∥Δ_(m−1)(t)|²/β_(m−1)(t−1)}  (59)

β_(m)(t)=β_(m−1)(t−1)−{|Δ_(m−1)(t)|²/ℑ_(m−1)(t)}  (60)

γ_(m)(t−1)=γ_(m−1)(t−1)−{|b_(m−1)(t−1)|²/β_(m−1)(t−1)}  (61)

ρ_(m,λa)(t)=λρ_(m,λa)(t−1)+{b _(m)(t)ε*_(m,λa)(t)/γ_(m)(t)}  (62)

ε_(m,λa)(t)={ρ_(m,λa)(t)/β_(m)(t)}  (63)

ε_(m+1,λa)(t)=ε_(m,λa)(t)−ε*_(m)(t)b _(m)(t)  (64)

where a (*) denotes a complex conjugate.

These equations cause the error signals f_(m)(t), b_(m)(t), e_(m,λa)(t)to be squared or to be multiplied by one another, in effect squaring theerrors, and creating new intermediate error values, such as Δ_(m−1)(t).The error signals and the intermediate error values are recursively tiedtogether, as shown in the above equations (54) through (64). Theyinteract to minimize the error signals in the next stage.

After a good approximation to either the primary signal s_(λa)(t) or thesecondary signal n_(λa)(t) has been determined by the joint processestimator 60, a next set of samples, including a sample of the measuredsignal S_(λa)(t) and a sample of either the secondary reference n′(t) orthe primary reference s′(t), are input to the joint process estimator60. The re-initialization process does not re-occur, such that theforward and backward reflection coefficient Γ_(f,m)(t) and Γ_(b,m)(t)register 90, 92 values and the regression coefficient κ_(m,λa)(t)register 96 value reflect the multiplicative values required to estimateeither the primary signal portion s_(λa)(t) or the secondary signalportion n_(λa)(t) of the sample of S_(λa)(t) input previously. Thus,information from previous samples is used to estimate either the primaryor secondary signal portion of a present set of samples in each stage.

In a more numerically stable and preferred embodiment of the abovedescribed joint process estimator, a normalized joint process estimatoris used. This version of the joint process estimator normalizes severalvariables of the above-described joint process estimator such that thenormalized variables fall between −1 and 1. The derivation of thenormalized joint process estimator is motivated in the Haykin text asproblem 12 on page 640 by redefining the variables defined according tothe following conditions:

${{\overset{\_}{f}}_{m}(t)} = \frac{f_{m}(t)}{\sqrt{{_{m}(t)}{\gamma_{m}\left( {t - 1} \right)}}}$${\overset{\_}{b}(t)} = \frac{b_{m}(t)}{\sqrt{{\beta_{m}(t)}{\gamma_{m}(t)}}}$${{\overset{\_}{\Delta}}_{m}(t)} = \frac{\Delta_{m}(t)}{\sqrt{{_{m}(t)}{\beta_{m}\left( {t - 1} \right)}}}$

This transformation allows the conversion of Equations (54)-(64) to thefollowing normalized equations:

${{\overset{\_}{\Delta}}_{m - 1}(t)} = {{{{{\overset{\_}{\Delta}}_{m - 1}\left( {t - 1} \right)}\left\lbrack {1 - {{f_{m - 1}(t)}}^{2}} \right\rbrack}^{1/2}\left\lbrack {1 - {{{\overset{\_}{b}}_{m - 1}\left( {t - 1} \right)}}^{2}} \right\rbrack}^{1/2} + {{{\overset{\_}{b}}_{m - 1}\left( {t - 1} \right)}{{\overset{\_}{f}}_{m - 1}(t)}}}$$\mspace{20mu} {{{\overset{\_}{b}}_{m}(t)} = \frac{\left\lbrack {{{\overset{\_}{b}}_{m - 1}\left( {t - 1} \right)} - {{{\overset{\_}{\Delta}}_{m - 1}(t)}{{\overset{\_}{f}}_{m - 1}(t)}}} \right\rbrack}{{\left\lbrack {1 - {{{\overset{\_}{\Delta}}_{m - 1}(t)}}^{2}} \right\rbrack^{1/2}\left\lbrack {1 - {{{\overset{\_}{f}}_{m - 1}(t)}}^{2}} \right\rbrack}^{1/2}}}$$\mspace{20mu} {{{\overset{\_}{f}}_{m}(t)} = \frac{\left\lbrack {{{\overset{\_}{f}}_{m - 1}(t)} - {{{\overset{\_}{\Delta}}_{m - 1}(t)}{{\overset{\_}{b}}_{m - 1}\left( {t - 1} \right)}}} \right\rbrack}{{\left\lbrack {1 - {{{\overset{\_}{\Delta}}_{m - 1}(t)}}^{2}} \right\rbrack^{1/2}\left\lbrack {1 - {{{\overset{\_}{b}}_{m - 1}\left( {t - 1} \right)}}^{2}} \right\rbrack}^{1/2}}}$$\mspace{20mu} {{\beta_{m}(t)} = {\left\lbrack {1 - {{{\overset{\_}{\Delta}}_{m - 1}(t)}}^{2}} \right\rbrack {\beta_{m - 1}\left( {t - 1} \right)}}}$$\mspace{20mu} {{\gamma_{m}(t)} = {{\gamma_{m - 1}(t)}\left\lbrack {1 - {{{\overset{\_}{b}}_{m - 1}(t)}}^{2}} \right\rbrack}}$$\mspace{20mu} {{\rho_{m}(t)} = {{{\lambda \cdot \left\lbrack \frac{{\gamma_{m}(t)}{\beta_{m}\left( {t - 1} \right)}}{{\gamma_{m}\left( {t - 1} \right)}{\beta_{m}(t)}} \right\rbrack^{1/2}}{\rho_{m}\left( {t - 1} \right)}} + {{{\overset{\_}{b}}_{m}(t)}{ɛ_{m}(t)}}}}$$\mspace{20mu} {{ɛ_{{m + 1},{\lambda \; a}}(t)} = {{ɛ_{m,{{\cdot \lambda}\; a}}(t)} - {{\rho_{m}(t)}{{\overset{\_}{b}}_{m}(t)}}}}$

Initialization of Normalized Joint Process Estimator

Let N(t) be defined as the reference noise input at time index n andU(t) be defined as combined signal plus noise input at time index t thefollowing equations apply (see Haykin, p. 619):

1. To initialize the algorithm, at time t=0 set

Δ _(m−1)(0)=0

β_(m−1)(0)=δ=10⁻⁶

γ₀(0)=1

2. At each instant t≧1, generate the various zeroth-order variables asfollows:

γ₀(t − 1) = 1 β₀(t) = λβ₀(t − 1) + N²(t)${{\overset{\_}{b}}_{0}(t)} = {{{\overset{\_}{f}}_{0}(t)} = \frac{N(t)}{\sqrt{\beta_{0\;}(t)}}}$

3. For regression filtering, initialize the algorithm by setting at timeindex t=0

ρ_(m)(0)=0

4. At each instant t≧1, generate the zeroth-order variable

ε₀(t)=U(t).

Accordingly, a normalized joint process estimator can be used for a morestable system.

In yet another embodiment, the correlation cancellation is performedwith a QRD algorithm as shown diagrammatically in FIG. 8 a and asdescribed in detail in Chapter 18 of Adaptive Filter Theory by SimonHaykin, published by Prentice-Hall, copyright 1986.

The following equations adapted from the Haykin book correspond to theQRD-LSL diagram of FIG. 8 a (also adapted from the Haykin book).

Computations

a. Predictions: For time t=1, 2, . . . , and prediction order m=1, 2, .. . , M, where M is the final prediction order, compute:

β_(m − 1)(t − 1) = λ β_(m − 1)(t − 2) + ɛ_(b, m − 1)(t − 1)²${c_{b,{m - 1}}\left( {t + 1} \right)} = \frac{\lambda^{1/2}{\beta_{m - 1}^{1/2}\left( {t - 2} \right)}}{\beta_{m - 1}^{1/2}\left( {t - 1} \right)}$${s_{b,{m - 1}}\left( {t - 1} \right)} = \frac{ɛ_{b,{m - 1}}^{\bullet}\left( {t - 1} \right)}{\beta_{m - 1}^{1/2}\left( {t - 1} \right)}$ɛ_(f, m)(t) = c_(b, m − 1)(t − 1)ɛ_(f, m − 1)(t) − s_(b, m − 1)^(•)(t − 1)λ^(1/2)π_(f, m − 1)^(•)(t − 1)π_(f, m − 1)^(•)(t) = c_(b, m − 1)(t − 1)λ^(1/2)π_(f, m − 1)^(•)(t − 1) + s_(b, m − 1)(t − 1)ɛ_(f, m − 1)(t)γ_(m)^(1/2)(t − 1) = c_(b, m − 1)(t − 1)γ_(m − 1)^(1/2)(t − 1)_(m − 1)(t) = λ _(m − 1)(t − 1) + ɛ_(f, m − 1)(t)²${c_{f,{m - 1}}(t)} = \frac{\lambda^{1/2}{_{m - 1}^{1/2}\left( {t - 1} \right)}}{_{m - 1}^{1/2}(t)}$${s_{f,{m - 1}}(t)} = \frac{ɛ_{f,{m - 1}}^{\bullet}(t)}{_{m - 1}^{1/2}(t)}$ɛ_(b, m)(t) = c_(f, m − 1)(t)ɛ_(b, m − 1)(t − 1) − s_(f, m − 1)^(•)(t)λ^(1/2)π_(b, m − 1)^(•)(t − 1)π_(b, m − 1)^(•)(t) = c_(f, m − 1)(t)λ^(1/2)π_(b, m − 1)^(•)(t − 1) + s_(f, m − 1)(t)ɛ_(b, m − 1)(t − 1)

b. Filtering: For order m=0, 1, . . . , M−1; and time t=1, 2, . . . ,compute

β_(m)(t) = λ β_(m)(t − 1) + ɛ_(b, m)(t)²${c_{b,m}(t)} = \frac{\lambda^{1/2}{\beta_{m}^{1/2}\left( {t - 1} \right)}}{\beta_{m}^{1/2}(t)}$${s_{b,m}(t)} = \frac{ɛ_{b,m}^{\bullet}(t)}{\beta_{m}^{1/2}(t)}$ɛ_(m + 1)(t) = c_(b, m)(t)ɛ_(m)(t) − s_(b, m)^(•)(t)λ^(1/2)ρ_(m)^(•)(t − 1)ρ_(m)^(•)(t) = c_(b, m)(t)λ^(1/2)ρ_(m)^(*)(t − 1) + s_(b, m)(t)ɛ_(m)(t)γ_(m+1) ^(1/2)(t)=c _(b,m)(t)γ_(m) ^(1/2)(t)

ε_(m+1)(t)=λ_(m+1) ^(1/2)(t)ε_(m+1)(t)

5. Initialization

a. Auxiliary parameter initialization: for order m=1, 2, . . . , M, set

π_(f,m−1)(0)=π_(b,m−1)(0)=0

p _(m)(0)=0

b. Soft constraint initialization: For order m=0, 1, . . . , M, set

β_(m)(−1)=δ

ℑ_(m)(0)=δ

where δ is a small positive constant.

c. Data initialization: For t=1, 2, . . . , compute

ε_(f,0)(t)=ε_(b,0)(t)=μ(t)

ε₀(t)=d(t)

γ₀(t)=1

where μ(t) is the input and d(t) is the desired response at time t.

Flowchart of Joint Process Estimator

In a signal processor, such as a physiological monitor incorporating areference processor of the present invention to determine a referencen′(t) or s′(t) for input to a correlation canceler, a joint processestimator 60 type adaptive noise canceler is generally implemented via asoftware program having an iterative loop. One iteration of the loop isanalogous to a single stage of the joint process estimator as shown inFIG. 8. Thus, if a loop is iterated m times, it is equivalent to an mstage joint process estimator 60.

A flow chart of a subroutine to estimate the primary signal portions_(λa)(t) or the secondary signal portion n_(λa)(t) of a measuredcomposite signal, S_(λa)(t) is shown in FIG. 9. The flow chartillustrates the function of a reference processor for determining eitherthe secondary reference n′(t) or the primary reference s′(t). Theflowchart for the joint process estimator is implemented in software.

A one-time initialization is performed when the physiological monitor ispowered-on, as indicated by an “INITIALIZE NOISE CANCELER” action block120. The initialization sets all registers 90, 92, and 96 and delayelement variables 110 to the values described above in equations (46)through (50).

Next, a set of simultaneous samples of the composite measured signalsS_(λa)(t) and S_(λb)(t) is input to the subroutine represented by theflowchart in FIG. 9. Then a time update of each of the delay elementprogram variables occurs, as indicated in a “TIME UPDATE OF [Z⁻¹]ELEMENTS” action block 130. The value stored in each of the delayelement variables 110 is set to the value at the input of the delayelement variable 110. Thus, the zero-stage backward prediction errorb₀(t) is stored as the first-stage delay element variable, and thefirst-stage backward prediction error b₁(t) is stored as thesecond-stage delay element variable, and so on.

Then, using the set of measured signal samples S_(λa)(t) and S_(λb)(t),the reference signal is obtained using the ratiometric or the constantsaturation methods described above. This is indicated by a “CALCULATEREFERENCE [n′(t) or s′(t)] FOR TWO MEASURED SIGNAL SAMPLES” action block140.

A zero-stage order update is performed next as indicated in a“ZERO-STAGE UPDATE” action block 150. The zero-stage backward predictionerror b₀(t), and the zero-stage forward prediction error f₀(t) are setequal to the value of the reference signal n′(t) or s′(t). Additionally,the weighted sum of the forward prediction errors ℑ_(m)(t) and theweighted sum of backward prediction errors β_(m)(t) are set equal to thevalue defined in equations (47) and (48).

Next, a loop counter, m, is initialized as indicated in a “m=0” actionblock 160. A maximum value of m, defining the total number of stages tobe used by the subroutine corresponding to the flowchart in FIG. 9, isalso defined. Typically, the loop is constructed such that it stopsiterating once a criterion for convergence upon a best approximation toeither the primary signal or the secondary signal has been met by thejoint process estimator 60. Additionally, a maximum number of loopiterations may be chosen at which the loop stops iteration. In apreferred embodiment of a physiological monitor of the presentinvention, a maximum number of iterations, m=6 to m=10, isadvantageously chosen.

Within the loop, the forward and backward reflection coefficientΓ_(f,m)(t) and Γ_(b,m)(t) register 90 and 92 values in the least-squareslattice filter are calculated first, as indicated by the “ORDER UPDATEMTH CELL OF LSL-LATTICE” action block 170 in FIG. 9. This requirescalculation of intermediate variable and signal values used indetermining register 90, 92, and 96 values in the present stage, thenext stage, and in the regression filter 80.

The calculation of regression filter register 96 value κ_(m,λa)(t) isperformed next, indicated by the “ORDER UPDATE MTH STAGE OF REGRESSIONFILTER(S)” action block 180. The two order update action blocks 170 and180 are performed in sequence m times, until m has reached itspredetermined maximum (in the preferred embodiment, m=6 to m=10) or asolution has been converged upon, as indicated by a YES path from a“DONE” decision block 190. In a computer subroutine, convergence isdetermined by checking if the weighted sums of the forward and backwardprediction errors ℑ_(m)(t) and β_(m)(t) are less than a small positivenumber. An output is calculated next, as indicated by a “CALCULATEOUTPUT” action block 200. The output is a good approximation to eitherthe primary signal or secondary signal, as determined by the referenceprocessor 26 and joint process estimator 60 subroutine corresponding tothe flow chart of FIG. 9. This is displayed (or used in a calculation inanother subroutine), as indicated by a “TO DISPLAY” action block 210.

A new set of samples of the two measured signals S_(λa)(t) and S_(λb)(t)is input to the processor and joint process estimator 60 adaptive noisecanceler subroutine corresponding to the flowchart of FIG. 9 and theprocess reiterates for these samples. Note, however, that theinitialization process does not re-occur. New sets of measured signalsamples S_(λa)(t) and S_(λb)(t) are continuously input to the referenceprocessor 26 and joint process estimator adaptive noise cancelersubroutine. The output forms a chain of samples which is representativeof a continuous wave. This waveform is a good approximation to eitherthe primary signal waveform s_(λa)(t) or the secondary waveformn_(λa)(t) at wavelength λ_(a). The waveform may also be a goodapproximation to either the primary signal waveform s_(λb)(t) or thesecondary waveform n″_(λb)(t) at wavelength λb.

A corresponding flowchart for the QRD algorithm of FIG. 8 a is depictedin FIG. 9 a, with reference numeral corresponding in number with an ‘a’extension.

Calculation of Saturation from Correlation Canceler Output

Physiological monitors may use the approximation of the primary signalss″_(λa)(t) or s″_(λb)(t) or the secondary signals n″_(λa)(t) orn″_(λb)(t) to calculate another quantity, such as the saturation of oneconstituent in a volume containing that constituent plus one or moreother constituents. Generally, such calculations require informationabout either a primary or secondary signal at two wavelengths. Forexample, the constant saturation method requires a good approximation ofthe primary signal portions s_(λa)(t) and s_(λb)(t) of both measuredsignals S_(λa)(t) and S_(λb)(t). The arterial saturation is determinedfrom the approximations to both signals, i.e. s″_(λa)(t) and s″_(λb)(t).The constant saturation method also requires a good approximation of thesecondary signal portions n_(λa)(t) or n_(λb)(t). An estimate of thevenous saturation may be determined from the approximations to thesesignals i.e. n″_(λa)(t) and n″_(λb)(t).

A joint process estimator 60 having two regression filters 80 a and 80 bis shown in FIG. 10. A first regression filter 80 a accepts a measuredsignal S_(λa)(t). A second regression filter 80 b accepts a measuredsignal S_(λb)(t) for a use of the constant saturation method todetermine the reference signal n′(t) or s′(t). The first and secondregression filters 80 a and 80 b are independent. The backwardprediction error b_(m)(t) is input to each regression filter 80 a and 80b, the input for the second regression filter 80 b bypassing the firstregression filter 80 a.

The second regression filter 80 b comprises registers 98, and summingelements 108 arranged similarly to those in the first regression filter80 a. The second regression filter 80 b operates via an additionalintermediate variable in conjunction with those defined by equations(54) through (64), i.e.:

ρ_(m,λb)(t)=λρ_(m,λb)(t−1)+{b _(m)(t)e* _(m,λb)(t)/γ_(m)(t)};  (65)

and

ρ_(0,λb)(0)=0.  (66)

The second regression filter 80 b has an error signal value definedsimilar to the first regression filter error signal values,e_(m+1,λa)(t), i.e.:

e _(m+1,λb)(t)=e _(m,λb)(t)−κ*_(m,λb)(t)b _(m)(t); and  (67)

e _(0,λb)(t)=S _(λb)(t) for t≧0.  (68)

The second regression filter has a regression coefficient κ_(m,λb)(t)register 98 value defined similarly to the first regression filter errorsignal values, i.e.:

κ_(m,λb)(t)={ρ_(m,λb)(t)/β_(m)(t)}; or  (69)

These values are used in conjunction with those intermediate variablevalues, signal values, register and register values defined in equations(46) through (64). These signals are calculated in an order defined byplacing the additional signals immediately adjacent a similar signal forthe wavelength λa.

For the constant saturation method, S_(λb)(t) is input to the secondregression filter 80 b. The output is then a good approximation to theprimary signal s″_(λb)(t) or secondary signal s″_(λb)(t).

The addition of the second regression filter 80 b does not substantiallychange the computer program subroutine represented by the flowchart ofFIG. 9. Instead of an order update of the m^(th) stage of only oneregression filter, an order update of the m^(th) stage of bothregression filters 80 a and 80 b is performed. This is characterized bythe plural designation in the “ORDER UPDATE OF m^(th) STAGE OFREGRESSION FILTER(S)” activity block 180 in FIG. 9. Since the regressionfilters 80 a and 80 b operate independently, independent calculationscan be performed in the reference processor and joint process estimator60 adaptive noise canceler subroutine modeled by the flowchart of FIG.9.

An alternative diagram for the joint process estimator of FIG. 10, usingthe QRD algorithm and having two regression filters is shown in FIG. 10a. This type of joint process estimator would be used for correlationcancellation using the QRD algorithm described in the Haykin book.

Calculation of Saturation

Once good approximations to the primary signal portions s″_(λa)(t) ands″_(λb)(t) or the secondary signal portion, n″_(λa)(t) and n″_(λb)(t),have been determined by the joint process estimator 60, the saturationof A₅ in a volume containing A₅ and A₆, for example, may be calculatedaccording to various known methods. Mathematically, the approximationsto the primary signals can be written in terms of λa and λb, as:

s″ _(λa)(t)≈ε_(5,λa) c ₅ x _(5,6)(t)+ε_(6,λa) c ₆ x _(5,6)(t);  (70)

and

s″ _(λb)(t)≈ε_(5,λb) c ₅ x _(5,6)(t)+ε_(6,λb) c ₆ x _(5,6)(t)  (71)

Equations (70) and (71) are equivalent to two equations having threeunknowns, namely c₅(t), c₆(t) and x_(5,6)(t). The saturation can bedetermined by acquiring approximations to the primary or secondarysignal portions at two different, yet proximate times t₁ and t₂ overwhich the saturation of A₅ in the volume containing A₅ and A₆ and thesaturation of A₃ in the volume containing A₃ and A₄ does not changesubstantially. For example, for the primary signals estimated at timest₁ and t₂:

s″ _(λa)(t ₁)≈ε_(5,λa) c ₅ x _(5,6)(t ₁)+ε_(6,λa) c ₆ x _(5,6)(t₁)  (72)

s″ _(λb)(t ₁)≈ε_(5,λb) c ₅ x _(5,6)(t ₁)+ε_(6,λb) c ₆ x _(5,6)(t₁)  (73)

s″ _(λa)(t ₂)≈ε_(5,λa) c ₅ x _(5,6)(t ₂)+ε_(6,λa) c ₆ x _(5,6)(t₂)  (74)

s″ _(λb)(t ₂)≈ε_(5,λb) c ₅ x _(5,6)(t ₂)+ε_(6,λb) c ₆ x _(5,6)(t₂)  (75)

Then, difference signals may be determined which relate the signals ofequations (72) through (75), i.e.:

Δs _(λa) =s″ _(λa)(t ₁)−s″ _(λa)(t ₂)≈ε_(5,λa) c ₅ Δx+ε _(6,λa) c ₆ Δx;and  (76)

Δs _(λb) =s″ _(λb)(t ₁)−s″ _(λb)(t ₂)≈ε_(5,λb) c ₅ Δx+ε _(,λb) c ₆Δx;  (77)

where Δx=x_(5,6)(t₁)−x_(5,6)(t₂). The average saturation at timet=(t₁+t₂)/2 is:

$\begin{matrix}\begin{matrix}{{{Saturation}(t)} = \frac{c_{5}(t)}{\left\lbrack {{c_{5}(t)} + {c_{6}(t)}} \right\rbrack}} \\{= {\frac{ɛ_{6,{\lambda \; a}} - {ɛ_{6,{\lambda \; b}}\left( {\Delta \; {s_{\lambda \; a}/\Delta}\; s_{\lambda \; b}} \right)}}{ɛ_{6,{\lambda \; a}} - ɛ_{5,{\lambda \; a}} - {\left( {ɛ_{6,{\lambda \; b}} - ɛ_{5,{\lambda \; b}}} \right)\left( {\Delta \; {s_{\lambda \; a}/\Delta}\; s_{\lambda \; b}} \right)}}(79)}}\end{matrix} & (78)\end{matrix}$

It will be understood that the Δx term drops out from the saturationcalculation because of the division. Thus, knowledge of the thickness ofthe primary constituents is not required to calculate saturation.

Pulse Oximetry Measurements

A specific example of a physiological monitor utilizing a processor ofthe present invention to determine a secondary reference n′(t) for inputto a correlation canceler that removes erratic motion-induced secondarysignal portions is a pulse oximeter. Pulse oximetry may also beperformed utilizing a processor of the present invention to determine aprimary signal reference s′(t) which may be used for display purposes orfor input to a correlation canceler to derive information about patientmovement and venous blood oxygen saturation.

A pulse oximeter typically causes energy to propagate through a mediumwhere blood flows close to the surface for example, an ear lobe, or adigit such as a finger, a forehead or a fetus' scalp. An attenuatedsignal is measured after propagation through or reflected from themedium. The pulse oximeter estimates the saturation of oxygenated blood.

Freshly oxygenated blood is pumped at high pressure from the heart intothe arteries for use by the body. The volume of blood in the arteriesvaries with the heartbeat, giving rise to a variation in absorption ofenergy at the rate of the heartbeat, or the pulse.

Oxygen depleted, or deoxygenated, blood is returned to the heart by theveins along with unused oxygenated blood. The volume of blood in theveins varies with the rate of breathing, which is typically much slowerthan the heartbeat. Thus, when there is no motion induced variation inthe thickness of the veins, venous blood causes a low frequencyvariation in absorption of energy. When there is motion inducedvariation in the thickness of the veins, the low frequency variation inabsorption is coupled with the erratic variation in absorption due tomotion artifact.

In absorption measurements using the transmission of energy through amedium, two light emitting diodes (LED's) are positioned on one side ofa portion of the body where blood flows close to the surface, such as afinger, and a photodetector is positioned on the opposite side of thefinger. Typically, in pulse oximetry measurements, one LED emits avisible wavelength, preferably red, and the other LED emits an infraredwavelength. However, one skilled in the art will realize that otherwavelength combinations could be used. The finger comprises skin,tissue, muscle, both arterial blood and venous blood, fat, etc., each ofwhich absorbs light energy differently due to different absorptioncoefficients, different concentrations, different thicknesses, andchanging optical pathlengths. When the patient is not moving, absorptionis substantially constant except for the flow of blood. The constantattenuation can be determined and subtracted from the signal viatraditional filtering techniques. When the patient moves, this causesperturbation such as changing optical pathlength due to movement ofbackground fluids (e.g., venous blood having a different saturation thanthe arterial blood). Therefore, the measured signal becomes erratic.Erratic motion induced noise typically cannot be predetermined and/orsubtracted from the measured signal via traditional filteringtechniques. Thus, determining the oxygen saturation of arterial bloodand venous blood becomes more difficult.

A schematic of a physiological monitor for pulse oximetry is shown inFIGS. 11-13. FIG. 11 depicts a general hardware block diagram of a pulseoximeter 299. A sensor 300 has two light emitters 301 and 302 such asLED's. One LED 301 emitting light of red wavelengths and another LED 302emitting light of infrared wavelengths are placed adjacent a finger 310.A photodetector 320, which produces an electrical signal correspondingto the attenuated visible and infrared light energy signals is locatedopposite the LED's 301 and 302. The photodetector 320 is connected tofront end analog signal conditioning circuitry 330.

The front end analog signal conditioning circuitry 330 has outputscoupled to analog to digital conversion circuit 332. The analog todigital conversion circuitry 332 has outputs coupled to a digital signalprocessing system 334. The digital signal processing system 334 providesthe desired parameters as outputs for a display 336. Outputs for displayare, for example, blood oxygen saturation, heart rate, and a cleanplethysmographic waveform.

The signal processing system also provides an emitter current controloutput 337 to a digital-to-analog converter circuit 338 which providescontrol information for light emitter drivers 340. The light emitterdrivers 340 couple to the light emitters 301, 302. The digital signalprocessing system 334 also provides a gain control output 342 for thefront end analog signal conditioning circuitry 330.

FIG. 11 a illustrates a preferred embodiment for the combination of theemitter drivers 340 and the digital to analog conversion circuit 338. Asdepicted in FIG. 11 a, the driver comprises first and second inputlatches 321, 322, a synchronizing latch 323, a voltage reference 324, adigital to analog conversion circuit 325, first and second switch banks326, 327, first and second voltage to current converters 328, 329 andthe LED emitters 301, 302 corresponding to the LED emitters 301, 302 ofFIG. 11.

The preferred driver depicted in FIG. 11 a is advantageous in that thepresent inventors recognized that much of the noise in the oximeter 299of FIG. 11 is caused by the LED emitters 301, 302. Therefore, theemitter driver circuit of FIG. 11 a is designed to minimize the noisefrom the emitters 301, 302. The first and second input latches 321, 324are connected directly to the DSP bus. Therefore, these latchessignificantly minimizes the bandwidth (resulting in noise) present onthe DSP bus which passes through to the driver circuitry of FIG. 11 a.The output of the first and second input latches only changes when theselatched detect their address on the DSP bus. The first input latchreceives the setting for the digital to analog converter circuit 325.The second input latch receives switching control data for the switchbanks 326, 327. The synchronizing latch accepts the synchronizing pulseswhich maintain synchronization between the activation of emitters 301,302 and the analog to digital conversion circuit 332.

The voltage reference is also chosen as a low noise DC voltage referencefor the digital to analog conversion circuit 325. In addition, in thepresent embodiment, the voltage reference has an lowpass output filterwith a very low corner frequency (e.g., 1 Hz in the present embodiment).The digital to analog converter 325 also has a lowpass filter at itsoutput with a very low corner frequency (e.g., 1 Hz). The digital toanalog converter provides signals for each of the emitters 301, 302.

In the present embodiment, the output of the voltage to currentconverters 328, 329 are switched such that with the emitters 301, 302connected in back-to-back configuration, only one emitter is active anany given time. In addition, the voltage to current converter for theinactive emitter is switched off at its input as well, such that it iscompletely deactivated. This reduces noise from the switching andvoltage to current conversion circuitry. In the present embodiment, lownoise voltage to current converters are selected (e.g., Op 27 Op Amps),and the feedback loop is configured to have a low pass filter to reducenoise. In the present embodiment, the low pass filtering function of thevoltage to current converter 328, 329 has a corner frequency of justabove 625 Hz, which is the switching speed for the emitters, as furtherdiscussed below. Accordingly, the preferred driver circuit of FIG. 11 a,minimizes the noise of the emitters 301, 302.

In general, the red and infrared light emitters 301, 302 each emitsenergy which is absorbed by the finger 310 and received by thephotodetector 320. The photodetector 320 produces an electrical signalwhich corresponds to the intensity of the light energy striking thephotodetector 320. The front end analog signal conditioning circuitry330 receives the intensity signals and filters and conditions thesesignals as further described below for further processing. The resultantsignals are provided to the analog-to-digital conversion circuitry 332which converts the analog signals to digital signals for furtherprocessing by the digital signal processing system 334. The digitalsignal processing system 334 utilizes the two signals in order toprovide a what will be called herein a “saturation transform.” It shouldbe understood, that for parameters other than blood saturationmonitoring, the saturation transform could be better termed as aconcentration transform, in-vivo transform, or the like, depending onthe desired parameter. The term saturation transform is used to describean operation which converts the sample data from time domain tosaturation domain values as will be apparent from the discussion below.In the present embodiment, the output of the digital signal processingsystem 334 provides clean plethysmographic waveforms of the detectedsignals and provides values for oxygen saturation and pulse rate to thedisplay 336.

It should be understood that in different embodiments of the presentinvention, one or more of the outputs may be provided. The digitalsignal processing system 334 also provides control for driving the lightemitters 301, 302 with an emitter current control signal on the emittercurrent control output 337. This value is a digital value which isconverted by the digital-to-analog conversion circuit 338 which providesa control signal to the emitter current drivers 340. The emitter currentdrivers 340 provide the appropriate current drive for the red emitter301 and the infrared emitter 302. Further detail of the operation of thephysiological monitor for pulse oximetry is explained below. In thepresent embodiment, the light emitters are driven via the emittercurrent driver 340 to provide light transmission with digital modulationat 625 Hz. In the present embodiment, the light emitters 301, 302 aredriven at a power level which provides an acceptable intensity fordetection by the detector and for conditioning by the front end analogsignal conditioning circuitry 330. Once this energy level is determinedfor a given patient by the digital signal processing system 334, thecurrent level for the red and infrared emitters is maintained constant.It should be understood, however, that the current could be adjusted forchanges in the ambient room light and other changes which would effectthe voltage input to the front end analog signal conditioning circuitry330. In the present invention, the red and infrared light emitters aremodulated as follows: for one complete 625 Hz red cycle, the red emitter301 is activated for the first quarter cycle, and off for the remainingthree-quarters cycle; for one complete 625 Hz infrared cycle, theinfrared light emitter 302 is activated for one quarter cycle and is offfor the remaining three-quarters cycle. In order to only receive onesignal at a time, the emitters are cycled on and off alternatively, insequence, with each only active for a quarter cycle per 625 Hz cycle anda quarter cycle separating the active times.

The light signal is attenuated (amplitude modulated) by the pumping ofblood through the finger 310 (or other sample medium). The attenuated(amplitude modulated) signal is detected by the photodetector 320 at the625 Hz carrier frequency for the red and infrared light. Because only asingle photodetector is used, the photodetector 320 receives both thered and infrared signals to form a composite time division signal.

The composite time division signal is provided to the front analogsignal conditioning circuitry 330. Additional detail regarding the frontend analog signal conditioning circuitry 330 and the analog to digitalconverter circuit 332 is illustrated in FIG. 12. As depicted in FIG. 12,the front end circuitry 302 has a preamplifier 342, a high pass filter344, an amplifier 346, a programmable gain amplifier 348, and a low passfilter 350. The preamplifier 342 is a transimpedance amplifier thatconverts the composite current signal from the photodetector 320 to acorresponding voltage signal, and amplifies the signal. In the presentembodiment, the preamplifier has a predetermined gain to boost thesignal amplitude for ease of processing. In the present embodiment, thesource voltages for the preamplifier 342 are −15 VDC and +15 VDC. Aswill be understood, the attenuated signal contains a componentrepresenting ambient light as well as the component representing theinfrared or the red light as the case may be in time. If there is lightin the vicinity of the sensor 300 other than the red and infrared light,this ambient light is detected by the photodetector 320. Accordingly,the gain of the preamplifier is selected in order to prevent the ambientlight in the signal from saturating the preamplifier under normal andreasonable operating conditions.

In the present embodiment, the preamplifier 342 comprises an AnalogDevices AD743JR OpAmp. This transimpedance amplifier is particularlyadvantageous in that it exhibits several desired features for the systemdescribed, such as: low equivalent input voltage noise, low equivalentinput current noise, low input bias current, high gain bandwidthproduct, low total harmonic distortion, high common mode rejection, highopen loop gain, and a high power supply rejection ratio.

The output of the preamplifier 342 couples as an input to the high passfilter 344. The output of the preamplifier also provides a first input346 to the analog to digital conversion circuit 332. In the presentembodiment, the high pass filter is a single-pole filter with a cornerfrequency of about ½-1 Hz. However, the corner frequency is readilyraised to about 90 Hz in one embodiment. As will be understood, the 625Hz carrier frequency of the red and infrared signals is well above a 90Hz corner frequency. The high-pass filter 344 has an output coupled asan input to an amplifier 346. In the present embodiment, the amplifier346 comprises a unity gain amplifier. However, the gain of the amplifier346 is adjustable by the variation of a single resistor. The gain of theamplifier 346 would be increased if the gain of the preamplifier 342 isdecreased to compensate for the effects of ambient light.

The output of the amplifier 346 provides an input to a programmable gainamplifier 348. The programmable gain amplifier 348 also accepts aprogramming input from the digital signal processing system 334 on again control signal line 343. The gain of the programmable gainamplifier 348 is digitally programmable. The gain is adjusteddynamically at initialization or sensor placement for changes in themedium under test from patient to patient. For example, the signal fromdifferent fingers differs somewhat. Therefore, a dynamically adjustableamplifier is provided by the programmable gain amplifier 348 in order toobtain a signal suitable for processing.

The programmable gain amplifier is also advantageous in an alternativeembodiment in which the emitter drive current is held constant. In thepresent embodiment, the emitter drive current is adjusted for eachpatient in order to obtain the proper dynamic range at the input of theanalog to digital conversion circuit 332. However, changing the emitterdrive current can alter the emitter wavelength, which in turn affectsthe end result in oximetry calculations. Accordingly, it would beadvantageous to fix the emitter drive current for all patients. In analternative embodiment of the present invention, the programmable gainamplifier can be adjusted by the DSP in order to obtain a signal at theinput to the analog to digital conversion circuit which is properlywithin the dynamic range (+3v to −3v in the present embodiment) of theanalog to digital conversion circuit 332. In this manner, the emitterdrive current could be fixed for all patients, eliminating thewavelength shift due to emitter current drive changes.

The output of the programmable gain amplifier 348 couples as an input toa low-pass filter 350. Advantageously, the low pass filter 350 is asingle-pole filter with a corner frequency of approximately 10 Khz inthe present embodiment. This low pass filter provides anti-aliasing inthe present embodiment.

The output of the low-pass filter 350 provides a second input 352 to theanalog-to-digital conversion circuit 332. FIG. 12 also depictsadditional defect of the analog-to-digital conversion circuit. In thepresent embodiment, the analog-to-digital conversion circuit 332comprises a first analog-to-digital converter 354 and a secondanalog-to-digital converter 356. Advantageously, the firstanalog-to-digital converter 354 accepts input from the first input 346to the analog-to-digital conversion circuit 332, and the second analogto digital converter 356 accepts input on the second input 352 to theanalog-to-digital conversion circuitry 332.

In one advantageous embodiment, the first analog-to-digital converter354 is a diagnostic analog-to-digital converter. The diagnostic task(performed by the digital signal processing system) is to read theoutput of the detector as amplified by the preamplifier 342 in order todetermine if the signal is saturating the input to the high-pass filter344. In the present embodiment, if the input to the high pass filter 344becomes saturated, the front end analog signal conditioning circuits 330provides a ‘0’ output. Alternatively, the first analog-to-digitalconverter 354 remains unused.

The second analog-to-digital converter 352 accepts the conditionedcomposite analog signal from the front end signal conditioning circuitry330 and converts the signal to digital form. In the present embodiment,the second analog to digital converter 356 comprises a single-channel,delta-sigma converter. In the present embodiment, a CrystalSemiconductor CS5317-KS delta-sigma analog to digital converter is used.Such a converter is advantageous in that it is low cost, and exhibitslow noise characteristics. More specifically, a delta-sigma converterconsists of two major portions, a noise modulator and a decimationfilter. The selected converter uses a second order analog delta-sigmamodulator to provide noise shaping. Noise shaping refers to changing thenoise spectrum from a flat response to a response where noise at thelower frequencies has been reduced by increasing noise at higherfrequencies. The decimation filter then cuts out the reshaped, higherfrequency noise to provide 16-bit performance at a lower frequency. Thepresent converter samples the data 128 times for every 16 bit data wordthat it produces. In this manner, the converter provides excellent noiserejection, dynamic range and low harmonic distortion, that help incritical measurement situations like low perfusion and electrocautery.

In addition, by using a single-channel converter, there is no need totune two or more channels to each other. The delta-sigma converter isalso advantageous in that it exhibits noise shaping, for improved noisecontrol. An exemplary analog to digital converter is a CrystalSemiconductor CS5317. In the present embodiment, the second analog todigital converter 356 samples the signal at a 20 Khz sample rate. Theoutput of the second analog to digital converter 356 provides datasamples at 20 Khz to the digital signal processing system 334 (FIG. 11).

The digital signal processing system 334 is illustrated in additionaldetail in FIG. 13. In the present embodiment, the digital signalprocessing system comprises a microcontroller 360, a digital signalprocessor 362, a program memory 364, a sample buffer 366, a data memory368, a read only memory 370 and communication registers 372. In thepresent embodiment, the digital signal processor 362 is an AnalogDevices AD 21020. In the present embodiment, the microcontroller 360comprises a Motorola 68HCO5, with built in program memory. In thepresent embodiment, the sample buffer 366 is a buffer which accepts the20 Khz sample data from the analog to digital conversion circuit 332 forstorage in the data memory 368. In the present embodiment, the datamemory 368 comprises 32 KWords (words being 40 bits in the presentembodiment) of static random access memory.

The microcontroller 360 is connected to the DSP 362 via a conventionalJTAG Tap line. The microcontroller 360 transmits the boot loader for theDSP 362 to the program memory 364 via the Tap line, and then allows theDSP 362 to boot from the program memory 364. The boot loader in programmemory 364 then causes the transfer of the operating instructions forthe DSP 362 from the read only memory 370 to the program memory 364.Advantageously, the program memory 364 is a very high speed memory forthe DSP 362.

The microcontroller 360 provides the emitter current control and gaincontrol signals via the communications register 372.

FIGS. 14-20 depict functional block diagrams of the operations of thepulse oximeter 299 carried out by the digital signal processing system334. The signal processing functions described below are carried out bythe DSP 362 in the present embodiment with the microcontroller 360providing system management. In the present embodiment, the operation issoftware/firmware controlled. FIG. 14 depicts a generalized functionalblock diagram for the operations performed on the 20 Khz sample dataentering the digital signal processing system 334. As illustrated inFIG. 14, a demodulation, as represented in a demodulation module 400, isfirst performed. Decimation, as represented in a decimation module 402is then performed on the resulting data. Certain statistics arecalculated, as represented in a statistics module 404 and a saturationtransform is performed, as represented in a saturation transform module406, on the data resulting from the decimation operation. The datasubjected to the statistics operations and the data subjected to thesaturation transform operations are forwarded to saturation operations,as represented by a saturation calculation module 408 and pulse rateoperations, as represented in a pulse rate calculation module 410.

In general, the demodulation operation separates the red and infraredsignals from the composite signal and removes the 625 Hz carrierfrequency, leaving raw data points. The raw data points are provided at625 Hz intervals to the decimation operation which reduces the samplesby an order of 10 to samples at 62.5 Hz. The decimation operation alsoprovides some filtering on the samples. The resulting data is subjectedto statistics and to the saturation transform operations in order tocalculate a saturation value which is very tolerant to motion artifactsand other noise in the signal. The saturation value is ascertained inthe saturation calculation module 408, and a pulse rate and a cleanplethysmographic waveform is obtained through the pulse rate module 410.Additional detail regarding the various operations is provided inconnection with FIGS. 15-21.

FIG. 15 illustrates the operation of the demodulation module 400. Themodulated signal format is depicted in FIG. 15. One full 625 Hz cycle ofthe composite signal is depicted in FIG. 15 with the first quarter cyclebeing the active red light plus ambient light signal, the second quartercycle being an ambient light signal, the third quarter cycle being theactive infrared plus ambient light signal, and the fourth quarter cyclebeing an ambient light signal. As depicted in FIG. 15, with a 20 KHzsampling frequency, the single full cycle at 625 Hz described abovecomprises 32 samples of 20 KHz data, eight samples relating to red plusambient light, eight samples relating to ambient light, eight samplesrelating to infrared plus ambient light, and finally eight samplesrelated to ambient light.

Because the signal processing system 334 controls the activation of thelight emitters 300, 302, the entire system is synchronous. The data issynchronously divided (and thereby demodulated) into four 8-samplepackets, with a time division demultiplexing operation as represented ina demultiplexing module 421. One eight-sample packet 422 represents thered plus ambient light signal; a second eight-sample packet 424represents an ambient light signal; a third eight-sample packet 426represents the attenuated infrared light plus ambient light signal; anda fourth eight-sample packet 428 represents the ambient light signal. Aselect signal synchronously controls the demultiplexing operation so asto divide the time-division multiplexed composite signal at the input ofthe demultiplexer 421 into its four subparts.

A sum of the last four samples from each packet is then calculated, asrepresented in the summing operations 430, 432, 434, 436 of FIG. 15. Inthe present embodiment, the last four samples are used because a lowpass filter in the analog to digital converter 356 of the presentembodiment has a settling time. Thus, collecting the last four samplesfrom each 8-sample packet allows the previous signal to clear. Thissumming operation provides an integration operation which enhances noiseimmunity. The sum of the respective ambient light samples is thensubtracted from the sum of the red and infrared samples, as representedin the subtraction modules 438, 440. The subtraction operation providessome attenuation of the ambient light signal present in the data. In thepresent embodiment, it has been found that approximately 20 dBattenuation of the ambient light is provided by the operations of thesubtraction modules 438, 440. The resultant red and infrared sum valuesare divided by four, as represented in the divide by four modules 442,444. Each resultant value provides one sample each of the red andinfrared signals at 625 Hz.

It should be understood that the 625 Hz carrier frequency has beenremoved by the demodulation operation 400. The 625 Hz sample data at theoutput of the demodulation operation 400 is sample data without thecarrier frequency. In order to satisfy Nyquist sampling requirements,less than 20 Hz is needed (understanding that the human pulse is about25 to 250 beats per minute, or about 0.4 Hz-4 Hz). Accordingly, the 625Hz resolution is reduced to 62.5 Hz in the decimation operation.

FIG. 16 illustrates the operations of the decimation module 402. The redand infrared sample data is provided at 625 Hz to respective red andinfrared buffer/filters 450, 452. In the present embodiment, the red andinfrared buffer/filters are 519 samples deep. Advantageously, the bufferfilters 450, 452 function as continuous first-in, first-out buffers. The519 samples are subjected to low-pass filtering. Preferably, thelow-pass filtering has a cutoff frequency of approximately 7.5 Hz withattenuation of approximately—110 dB. The buffer/filters 450, 452 form aFinite Impulse Response (FIR) filter with coefficients for 519 taps. Inorder to reduce the sample frequency by ten, the low-pass filtercalculation is performed every ten samples, as represented in respectivered and infrared decimation by 10 modules 454, 456. In other words, withthe transfer of each new ten samples into the buffer/filters 450, 452, anew low pass filter calculation is performed by multiplying the impulseresponse (coefficients) by the 519 filter taps. Each filter calculationprovides one output sample for respective red and infrared outputbuffers 458, 460. In the present embodiment, the red and infrared outputbuffers 458, 460 are also continuous FIFO buffers that hold 570 samplesof data. The 570 samples provide respective infrared and red samples orpackets (also denoted “snapshot” herein) of samples. As depicted in FIG.14, the output buffers provide sample data for the statistics operationmodule 404, saturation transform module 406, and the pulse rate module410.

FIG. 17 illustrates additional functional operation details of thestatistics module 404. In summary, the statistics module 404 providesfirst order oximetry calculations and RMS signal values for the red andinfrared channels. The statistics module also provides across-correlation output which indicates a cross-correlation between thered and infrared signals.

As represented in FIG. 17, the statistics operation accepts two packetsof samples (e.g., 570 samples at 62.5 Hz in the present embodiment)representing the attenuated infrared and red signals, with the carrierfrequency removed. The respective packets for infrared and red signalsare normalized with a log function, as represented in the Log modules480, 482. The normalization is followed by removal of the DC portion ofthe signals, as represented in the DC Removal modules 484, 486. In thepresent embodiment, the DC removal involves ascertaining the DC value ofthe first one of the samples (or the mean of the first several or themean of an entire snapshot) from each of the respective red and infraredsnapshots, and removing this DC value from all samples in the respectivepackets.

Once the DC signal is removed, the signals are subjected to bandpassfiltering, as represented in red and infrared Bandpass Filter modules488, 490. In the present embodiment, with 570 samples in each packet,the bandpass filters are configured with 301 taps to provide a FIRfilter with a linear phase response and little or no distortion. In thepresent embodiment, the bandpass filter has a pass band from 34beats/minute to 250 beats/minute. The 301 taps slide over the 570samples in order to obtain 270 filtered samples representing thefiltered red signal and 270 filtered samples representing the filteredinfrared signal. In an ideal case, the bandpass filters 488, 490 removethe DC in the signal. However, the DC removal operations 484, 486 assistin DC removal in the present embodiment.

After filtering, the last 120 samples from each packet (of now 270samples in the present embodiment) are selected for further processingas represented in Select Last 120 Samples modules 492, 494. The last 120samples are selected because, in the present embodiment, the first 150samples fall within the settling time for the Saturation Transfer module406, which processes the same data packets, as further discussed below.

Conventional saturation equation calculations are performed on the redand infrared 120-sample packets. In the present embodiment, theconventional saturation calculations are performed in two differentways. For one calculation, the 120-sample packets are processed toobtain their overall RMS value, as represented in the first red andinfrared RMS modules 496, 498. The resultant RMS values for red andinfrared signals provide input values to a first RED_RMS/IR_RMS ratiooperation 500, which provides the RMS red value to RMS infrared valueratio as an input to a saturation equation module 502. As wellunderstood in the art, the ratio of the intensity of red to infraredattenuated light as detected for known red and infrared wavelengths(typically λ_(red)=650 nm and λ_(IR)=910 nm) relates to the oxygensaturation of the patient. Accordingly, the saturation equation module502 represents a conventional look-up table or the like which, forpredetermined ratios, provides known saturation values at its output504. The red and infrared RMS values are also provided as outputs of thestatistics operations module 404.

In addition to the conventional saturation operation 502, the 120-samplepackets are subjected to a cross-correlation operation as represented ina first cross-correlation module 506. The first cross-correlation module506 determines if good correlation exists between the infrared and redsignals. This cross correlation is advantageous for detecting defectiveor otherwise malfunctioning detectors. The cross correlation is alsoadvantageous in detecting when the signal model (i.e., the model ofEquations (1)-(3)) is satisfied. If correlation becomes too low betweenthe two channels, the signal model is not met. In order to determinethis, the normalized cross correlation can be computed by thecross-correlation module 506 for each snapshot of data. One suchcorrelation function is as follows:

$\frac{\sum{s_{1}s_{2}}}{\sqrt{\sum{s_{1}^{2}s_{2}^{2}}}}$

If the cross correlation is too low, the oximeter 299 provides a warning(e.g., audible, visual, etc.) to the operator. In the presentembodiment, if a selected snapshot yields a normalized correlation ofless than 0.75, the snapshot does not qualify. Signals which satisfy thesignal model will have a correlation greater than the threshold.

The red and infrared 120-sample packets are also subjected to a secondsaturation operation and cross correlation in the same manner asdescribed above, except the 120 samples are divided into 5 equal bins ofsamples (i.e., 5 bins of 24 samples each). The RMS, ratio, saturation,and cross correlation operations are performed on a bin-by-bin basis.These operations are represented in the Divide Into Five Equal Binsmodules 510, 512, the second red and infrared RMS modules 514, 516, thesecond RED-RMS/IR-RMS ratio module 518, the second saturation equationmodule 520 and the second cross correlation module 522 in FIG. 17.

FIG. 18 illustrates additional detail regarding the saturation transformmodule 406 depicted in FIG. 14. As illustrated in FIG. 18, thesaturation transform module 406 comprises a reference processor 530, acorrelation canceler 531, a master power curve module 554, and a binpower curve module 533. The saturation transform module 406 can becorrelated to FIG. 7 a which has a reference processor 26 and acorrelation canceler 27 and an integrator 29 to provide a power curvefor separate signal coefficients as depicted in FIG. 7 c. The saturationtransform module 406 obtains a saturation spectrum from the snapshots ofdata. In other words, the saturation transform 406 provides informationof the saturation values present in the snapshots.

As depicted in FIG. 18, the reference processor 530 for the saturationtransform module 406 has a saturation equation module 532, a referencegenerator module 534, a DC removal module 536 and a bandpass filtermodule 538. The red and infrared 570-sample packets from the decimationoperation are provided to the reference processor 530. In addition, aplurality of possible saturation values (the “saturation axis scan”) areprovided as input to the saturation reference processor 530. In thepresent embodiment, 117 saturation values are provided as the saturationaxis scan. In a preferred embodiment, the 117 saturation values rangeuniformly from a blood oxygen saturation of 34.8 to 105.0. Accordingly,in the present embodiment, the 117 saturation values provide an axisscan for the reference processor 530 which generates a reference signalfor use by the correlation canceler 531. In other words, the referenceprocessor is provided with each of the saturation values, and aresultant reference signal is generated corresponding to the saturationvalue. The correlation canceler is formed by a joint process estimator550 and a low pass filter 552 in the present embodiment.

It should be understood that the scan values could be chosen to providehigher or lower resolution than 117 scan values. The scan values couldalso be non-uniformly spaced.

As illustrated in FIG. 18, the saturation equation module 532 acceptsthe saturation axis scan values as an input and provides a ratio “r_(n)”as an output. In comparison to the general discussion of FIG. 7 a-7 c,this ratio “r_(n)” corresponds to the plurality of scan value discussedabove in general. The saturation equation simply provides a known ratio“r” (red/infrared) corresponding to the saturation value received as aninput.

The ratio “r_(n)” is provided as an input to the reference generator534, as are the red and infrared sample packets. The reference generator534 multiplies either the red or infrared samples by the ratio “r_(n)”and subtracts the value from the infrared or red samples, respectively.For instance, in the present embodiment, the reference generator 534multiplies the red samples by the ratio “r_(n)” and subtracts this valuefrom the infrared samples. The resulting values become the output of thereference generator 534. This operation is completed for each of thesaturation scan values (e.g., 117 possible values in the presentembodiment). Accordingly, the resultant data can be described as 117reference signal vectors of 570 data points each, hereinafter referredto as the reference signal vectors. This data can be stored in an arrayor the like.

In other words, assuming that the red and infrared sample packetsrepresent the red S_(red)(t) and infrared S_(IR)(t) measured signalswhich have primary s(t) and secondary n(t) signal portions, the outputof the reference generator becomes the secondary reference signal n′(t),which complies with the signal model defined above, as follows:

n′(t)=s _(ir)(t)−r _(n) s _(red)(t)

In the present embodiment, the reference signal vectors and the infraredsignal are provided as input to the DC removal module 536 of thereference processor 530. The DC removal module 536, like the DC removalmodules 484, 486 in the statistics module 404, ascertains the DC valueof the first of the samples for the respective inputs (or mean of thefirst several or all samples in a packet) and subtracts the respectiveDC baseline from the sample values. The resulting sample values aresubjected to a bandpass filter 538.

The bandpass filter 538 of the reference processor 530 performs the sametype of filtering as the bandpass filters 488, 490 of the statisticsmodule 404. Accordingly, each set of 570 samples subjected to bandpassfiltering results in 270 remaining samples. The resulting data at afirst output 542 of the bandpass filter 538 is one vector of 270 samples(representing the filtered infrared signal in the present embodiment).The resulting data at a second output 540 of the bandpass filter 538,therefore, is 117 reference signal vectors of 270 data points each,corresponding to each of the saturation axis scan values provided to thesaturation reference processor 530.

It should be understood that the red and infrared sample packets may beswitched in their use in the reference processor 530. In addition, itshould be understood that the DC removal module 536 and the bandpassfilter module 538 can be executed prior to input of the data to thereference processor 530 because the calculations performed in thereference processor are linear. This results in a significant processingeconomy.

The outputs of the reference processor 530 provide first and secondinputs to a joint process estimator 550 of the type described above withreference to FIG. 8. The first input to the joint process estimator 550is the 270-sample packet representing the infrared signal in the presentembodiment. This signal contains primary and secondary signal portions.The second input to the joint process estimator is the 117 referencesignal vectors of 270 samples each.

The joint process estimator also receives a lambda input 543, a minimumerror input 544 and a number of cells configuration input 545. Theseparameters are well understood in the art. The lambda parameter is oftencalled the “forgetting parameter” for a joint process estimator. Thelambda input 543 provides control for the rate of cancellation for thejoint process estimator. In the present embodiment, lambda is set to alow value such as 0.8. Because statistics of the signal arenon-stationary, a low value improves tracking. The minimum error input544 provides an initialization parameter (conventionally known as the“initialization value”) for the joint process estimator 550. In thepresent embodiment, the minimum error value is 10⁻⁶. This initializationparameter prevents the joint process estimator 500 from dividing by zeroupon initial calculations. The number of cells input 545 to the jointprocess estimator 550 configures the number of cells for the jointprocess estimator. In the present embodiment, the number of cells forthe saturation transform operation 406 is six. As well understood in theart, for each sine wave, the joint process estimator requires two cells.If there are two sine waves in the 35-250 beats/minute range, six cellsallows for the two heart beat sine waves and one noise sine wave.

The joint process estimator 550 subjects the first input vector on thefirst input 542 to a correlation cancellation based upon each of theplurality of reference signal vectors provided in the second input 540to the correlation canceler 531 (all 117 reference vectors in sequencein the present embodiment). The correlation cancellation results in asingle output vector for each of the 117 reference vectors. Each outputvector represents the information that the first input vector and thecorresponding reference signal vector do not have in common. Theresulting output vectors are provided as an output to the joint processestimator, and subjected to the low pass filter module 552. In thepresent embodiment, the low pass filter 552 comprises a FIR filter with25 taps and with a corner frequency of 10 Hz with the sampling frequencyof 62.5 Hz (i.e., at the decimation frequency).

The joint process estimator 550 of the present embodiment has a settlingtime of 150 data points. Therefore, the last 120 data points from each270 point output vector are used for further processing. In the presentembodiment, the output vectors are further processed together as awhole, and are divided into a plurality of bins of equal number of datapoints. As depicted in FIG. 18, the output vectors are provided to amaster power curve module 554 and to a Divide into five Equal Binsmodule 556. The Divide into Five Equal Bins module 556 divides each ofthe output vectors into five bins of equal number of data points (e.g.,with 120 data points per vector, each bin has 24 data points). Each binis then provided to the Bin Power Curves module 558.

The Master Power Curve module 554 performs a saturation transform asfollows: for each output vector, the sum of the squares of the datapoints is ascertained. This provides a sum of squares valuecorresponding to each output vector (each output vector corresponding toone of the saturation scan values). These values provide the basis for amaster power curve 555, as further represented in FIG. 22. Thehorizontal axis of the power curve represents the saturation axis scanvalues and the vertical axis represents the sum of squares value (oroutput energy) for each output vector. In other words, as depicted inFIG. 22, each of the sum of squares could be plotted with the magnitudeof the sum of squares value plotted on the vertical “energy output” axisat the point on the horizontal axis of the corresponding saturation scanvalue which generated that output vector. This results in a master powercurve 558, an example of which is depicted in FIG. 22. This provides asaturation transform in which the spectral content of the attenuatedenergy is examined by looking at every possible saturation value andexamining the output value for the assumed saturation value. As will beunderstood, where the first and second inputs to the correlationcanceler 531 are mostly correlated, the sum of squares for thecorresponding output vector of the correlation canceler 531 will be verylow. Conversely, where the correlation between the first and secondinputs to the correlation canceler 531 are not significantly correlated,the sum of squares of the output vector will be high. Accordingly, wherethe spectral content of the reference signal and the first input to thecorrelation canceler are made up mostly of physiological (e.g., movementof venous blood due to respiration) and non-physiological (e.g., motioninduced) noise, the output energy will be low. Where the spectralcontent of the reference signal and the first input to the correlationcanceler are not correlated, the output energy will be much higher.

A corresponding transform is completed by the Bin Power Curves module558, except a saturation transform power curve is generated for eachbin. The resulting power curves are provided as the outputs of thesaturation transform module 406.

In general, in accordance with the signal model of the presentinvention, there will be two peaks in the power curves, as depicted inFIG. 22. One peak corresponds to the arterial oxygen saturation of theblood, and one peak corresponds to the venous oxygen concentration ofthe blood. With reference to the signal model of the present invention,the peak corresponding to the highest saturation value (not necessarilythe peak with the greatest magnitude) corresponds to the proportionalitycoefficient r_(a). In other words, the proportionality coefficient r_(a)corresponds to the red/infrared ratio which will be measured for thearterial saturation. Similarly, peak that corresponds to the lowestsaturation value (not necessarily the peak with the lowest magnitude)will generally correspond to the venous oxygen saturation, whichcorresponds to the proportionality coefficient r_(v) in the signal modelof the present invention. Therefore, the proportionality coefficientr_(v) will be a red/infrared ratio corresponding to the venous oxygensaturation.

In order to obtain arterial oxygen saturation, the peak in the powercurves corresponding to the highest saturation value could be selected.However, to improve confidence in the value, further processing iscompleted. FIG. 19 illustrates the operation of the saturationcalculation module 408 based upon the output of the saturation transformmodule 406 and the output of the statistics module 404. As depicted inFIG. 19, the bin power curves and the bin statistics are provided to thesaturation calculation module 408. In the present embodiment, the masterpower curves are not provided to the saturation module 408 but can bedisplayed for a visual check on system operation. The bin statisticscontain the red and infrared RMS values, the seed saturation value, anda value representing the cross-correlation between the red and infraredsignals from the statistics module 404.

The saturation calculation module 408 first determines a plurality ofbin attributes as represented by the Compute Bin Attributes module 560.The Compute Bin Attributes module 560 collects a data bin from theinformation from the bin power curves and the information from the binstatistics. In the present embodiment, this operation involves placingthe saturation value of the peak from each power curve corresponding tothe highest saturation value in the data bin. In the present embodiment,the selection of the highest peak is performed by first computing thefirst derivative of the power curve in question by convolving the powercurve with a smoothing differentiator filter function. In the presentembodiment, the smoothing differentiator filter function (using a FIRfilter) has the following coefficients:

-   -   0.014964670230367    -   0.098294046682706    -   0.204468276324813    -   2.717182664241813    -   5.704485606695227    -   0.000000000000000    -   −5.704482606695227    -   −2.717182664241813    -   −0.204468276324813    -   −0.098294046682706    -   −0.014964670230367

This filter performs the differentiation and smoothing. Next, each pointin the original power curve in question is evaluated and determined tobe a possible peak if the following conditions are met: (1) the point isat least 2% of the maximum value in the power curve; (2) the value ofthe first derivative changes from greater than zero to less than orequal to zero. For each point that is found to be a possible peak, theneighboring points are examined and the largest of the three points isconsidered to be the true peak.

The peak width for these selected peaks is also calculated. The peakwidth of a power curve in question is computed by summing all the pointsin the power curve and subtracting the product of the minimum value inthe power curve and the number of points in the power curve. In thepresent embodiment, the peak width calculation is applied to each of thebin power curves. The maximum value is selected as the peak width.

In addition, the infrared RMS value from the entire snapshot, the redRMS value, the seed saturation value for each bin, and the crosscorrelation between the red and infrared signals from the statisticsmodule 404 are also placed in the data bin. The attributes are then usedto determine whether the data bin consists of acceptable data, asrepresented in a Bin Qualifying Logic module 562.

If the correlation between the red and infrared signals is too low, thebin is discarded. If the saturation value of the selected peak for agiven bin is lower than the seed saturation for the same bin, the peakis replaced with the seed saturation value. If either red or infraredRMS value is below a very small threshold, the bins are all discarded,and no saturation value is provided, because the measured signals areconsidered to be too small to obtain meaningful data. If no bins containacceptable data, the exception handling module 563 provides a message tothe display 336 that the data is erroneous.

If some bins qualify, those bins that qualify as having acceptable dataare selected, and those that do not qualify are replaced with theaverage of the bins that are accepted. Each bin is given a time stamp inorder to maintain the time sequence. A voter operation 565 examines eachof the bins and selects the three highest saturation values. Thesevalues are forwarded to a clip and smooth operation 566.

The clip and smooth operation 566 basically performs averaging with alow pass filter. The low pass filter provides adjustable smoothing asselected by a Select Smoothing Filter module 568. The Select SmoothingFilter module 568 performs its operation based upon a confidencedetermination performed by a High Confidence Test module 570. The highconfidence test is an examination of the peak width for the bin powercurves. The width of the peaks provides some indication of motion by thepatient—wider peaks indicating motion. Therefore, if the peaks are wide,the smoothing filter is slowed down. If peaks are narrow, the smoothingfilter speed is increased. Accordingly, the smoothing filter 566 isadjusted based on the confidence level. The output of the clip andsmooth module 566 provides the oxygen saturation values in accordancewith the present invention.

In the presently preferred embodiment, the clip and smooth filter 566takes each new saturation value and compares it to the currentsaturation value. If the magnitude of the difference is less than 16(percent oxygen saturation) then the value is pass. Otherwise, if thenew saturation value is less than the filtered saturation value, the newsaturation value is changed to 16 less than the filtered saturationvalue. If the new saturation value is greater than the filteredsaturation value, then the new saturation value is changed to 16 morethan the filtered saturation value.

During high confidence (no motion), the smoothing filter is a simpleone-pole or exponential smoothing filter which is computed as follows:

y(n)=0.6*x(n)+0.4*y(n−1)

where x(n) is the clipped new saturation value, and y(n) is the filteredsaturation value.

During motion condition, a three-pole IIR (infinite impulse response)filter is used. Its characteristics are controlled by three timeconstants t_(a), t_(b), and t _(c) with values of 0.985, 0.900, and 0.94respectively. The coefficients for a direct form I, IIR filter arecomputed from these time constants using the following relationships:

a ₀=0

a ₁ =t _(b)+(t _(c))(t _(a) +t _(b))

a ₂=(−t _(b))(t _(c))(t _(a) +t _(b)+(t _(c))(t _(a)))

a ₃=(t _(b))²(t _(c))²(t _(a))

b ₀=1−t _(b)−(t _(c))(t _(a)+(t _(c))(t _(b)))

b ₁=2(t _(b))(t _(c))(t _(a)−1)

b ₂=(t _(b))(t _(c))(t _(b)+(t _(c))(t _(a))−(t _(b))(t _(c))(t _(a))−t_(a))

FIGS. 20 and 21 illustrate the pulse rate module 410 (FIG. 14) ingreater detail. As illustrated in FIG. 20, the heart rate module 410 hasa transient removal and bandpass filter module 578, a motion artifactsuppression module 580, a saturation equation module 582, a motionstatus module 584, first and second spectral estimation modules 586,588, a spectrum analysis module 590, a slew rate limiting module 592, anoutput filter 594, and an output filter coefficient module 596.

As further depicted in FIG. 20, the heart rate module 410 accepts theinfrared and red 570-sample snapshots from the output of the decimationmodule 402. The heart rate module 410 further accepts the saturationvalue which is output from the saturation calculation module 408. Inaddition, the maximum peak width as calculated by the confidence testmodule 570 (same as peak width calculation described above) is alsoprovided as an input to the heart rate module 410. The infrared and redsample packets, the saturation value and the output of the motion statusmodule 584 are provided to the motion artifact suppression module 580.

The average peak width value provides an input to a motion status module584. In the present embodiment, if the peaks are wide, this is taken asan indication of motion. If motion is not detected, spectral estimationon the signals is carried out directly without motion artifactsuppression.

In the case of motion, motion artifacts are suppressed using the motionartifact suppression module 580. The motion artifact suppression module580 is nearly identical to the saturation transform module 406. Themotion artifact suppression module 580 provides an output which connectsas an input to the second spectral estimation module 588. The first andsecond spectral estimation modules 586, 588 have outputs which provideinputs to the spectrum analysis module 590. The spectrum analysis module590 also receives an input which is the output of the motion statusmodule 584. The output of the spectrum analysis module 590 is theinitial heart rate determination of the heart rate module 410 and isprovided as input to the slew rate limiting module 592. The slew ratelimiting module 592 connects to the output filter 594. The output filter594 also receives an input from the output filter coefficient module596. The output filter 594 provides the filtered heart rate for thedisplay 336 (FIG. 11).

In the case of no motion, one of the signals (the infrared signal in thepresent embodiment) is subjected to DC removal and bandpass filtering asrepresented in the DC removal and bandpass filter module 578. The DCremoval and bandpass filter module 578 provide the same filtering as theDC removal and bandpass filter modules 536, 538. During no motionconditions, the filtered infrared signal is provided to the firstspectral estimation module 586.

In the present embodiment, the spectral estimation comprises a Chirp Ztransform that provides a frequency spectrum of heart rate information.The Chirp Z transform is used rather than a conventional FourierTransform because a frequency range for the desired output can bedesignated in a Chirp Z transform. Accordingly, in the presentembodiment, a frequency spectrum of the heart rate is provided between30 and 250 beats/minute. In the present embodiment, the frequencyspectrum is provided to a spectrum analysis module 590 which selects thefirst harmonic from the spectrum as the pulse rate. Usually, the firstharmonic is the peak in the frequency spectrum that has the greatestmagnitude and represents the pulse rate. However, in certain conditions,the second or third harmonic can exhibit the greater magnitude. Withthis understanding, in order to select the first harmonic, the firstpeak that has an amplitude of at least 1/20th of the largest peak in thespectrum is selected). This minimizes the possibility of selecting asthe heart rate a peak in the Chirp Z transform caused by noise.

In the case of motion, a motion artifact suppression is completed on thesnapshot with the motion artifact suppression module 580. The motionartifact suppression module 580 is depicted in greater detail in FIG.21. As can be seen in FIG. 21, the motion artifact suppression module580 is nearly identical to the saturation transform module 406 (FIG.18). Accordingly, the motion artifact suppression module has a motionartifact reference processor 570 and a motion artifact correlationcanceler 571.

The motion artifact reference processor 570 is the same as the referenceprocessor 530 of the saturation transform module 406. However, thereference processor 570 utilizes the saturation value from thesaturation module 408, rather than completing an entire saturationtransform with the 117 saturation scan values. The reference processor570, therefore, has a saturation equation module 581, a referencegenerator 582, a DC removal module 583, and a bandpass filter module585. These modules are the same as corresponding modules in thesaturation transform reference processor 530. In the present embodiment,the saturation equation module 581 receives the arterial saturationvalue from the saturation calculation module 408 rather than doing asaturation axis scan as in the saturation transform module 406. This isbecause the arterial saturation has been selected, and there is no needto perform an axis scan. Accordingly, the output of the saturationequation module 581 corresponds to the proportionality constant r_(a)(i.e., the expected red to infrared ratio for the arterial saturationvalue). Otherwise, the reference processor 570 performs the samefunction as the reference processor 530 of the saturation transformmodule 406.

The motion artifact correlation canceler 571 is also similar to thesaturation transform correlation canceler 531 (FIG. 18). However, themotion artifact suppression correlation canceler 571 uses a slightlydifferent motion artifact joint process estimator 572. Accordingly, themotion artifact suppression correlation canceler 571 has a joint processestimator 572 and a low-pass filter 573. The motion artifact jointprocess estimator 572 differs from the saturation transform jointprocess estimator 550 in that there are a different number of cells(between 6 and 10 in the present embodiment), as selected by the Numberof Cells input 574, in that the forgetting parameter differs (0.98 inthe present embodiment), and in that the time delay due to adaptationdiffers. The low-pass filter 573 is the same as the low pass filter 552of the saturation transform correlation canceler 531.

Because only one saturation value is provided to the referenceprocessor, only one output vector of 270 samples results at the outputof the motion artifact suppression correlation canceler 571 for eachinput packet of 570 samples. In the present embodiment, where theinfrared wavelength is provided as a first input to the correlationcanceler, the output of the correlation canceler 571 provides a cleaninfrared waveform. It should be understood that, as described above, theinfrared and red wavelength signals could be switched such that a cleanred waveform is provided at the output of the motion artifactsuppression correlation canceler 571. The output of the correlationcanceler 571 is a clean waveform because the actual saturation value ofthe patient is known which allows the reference processor 570 togenerate a noise reference for inputting to the correlation canceler 571as the reference signal. The clean waveform at the output of the motionartifact suppression module 580 is a clean plethysmograph waveform whichcan be forwarded to the display 336.

As described above, an alternative joint process estimator uses the QRDleast squares lattice approach (FIGS. 8 a, 9 a and 10 a). Accordingly,the joint process estimator 573 (as well as the joint process estimator550) could be replaced with a joint process estimator executing the QRDleast squares lattice operation.

FIG. 21 a depicts an alternative embodiment of the motion artifactsuppression module with a joint process estimator 572 a replacing thejoint process estimator 572. The joint process estimator 572 a comprisesa QRD least squares lattice system as in FIG. 10 a. In accordance withthis embodiment, different initialization parameters are used asnecessary for the QRD algorithm.

The initialization parameters are referenced in FIG. 21 a as “Number ofCells,” “Lambda,” “MinSumErr,” “GamsInit,” and “SumErrInit.” Number ofCells and Lambda correspond to like parameters in the joint processestimator 572. GamsInit corresponds to the y initialization variable forall stages except the zero order stage, which as set forth in the QRDequations above is initialized to ‘1’. SummErrinit provides the 6initialization parameter referenced above in the QRD equations. In orderto avoid overflow, the larger of the actual calculated denominator ineach division in the QRD equations and MinSumErr is used. In the presentembodiment, the preferred initialization parameters are as follows:

-   -   Number of Cells=6    -   Lambda=0.8    -   MinSumErr=10⁻²⁰    -   GamsInit=10⁻²    -   SumErrInit=10⁻⁶.

The clean waveform output from the motion artifact suppression module580 also provides an input to the second spectral estimation module 588.The second spectral estimation module 588 performs the same Chirp Ztransform as the first spectral estimation module 586. In the case of nomotion, the output from the first spectral estimation module 586 isprovided to the spectrum analysis module 586; in the case of motion, theoutput from the second spectral estimation module 588 is provided to aspectrum analysis module 590. The spectrum analysis module 590 examinesthe frequency spectrum from the appropriate spectral estimation moduleto determine the pulse rate. In the case of motion, the spectrumanalysis module 590 selects the peak in the spectrum with the highestamplitude, because the motion artifact suppression module 580 attenuatesall other frequencies to a value below the actual heart rate peak. Inthe case of no motion, the spectrum analysis module selects the firstharmonic in the spectrum as the heart rate as described above.

The output of the spectrum analysis module 590 provides the raw heartrate as an input to the slew rate limiting module 592, which provides aninput to an output filter 594. In the present embodiment, the slew ratelimiting module 592 prevents changes greater that 20 beats/minute per 2second interval.

The output filter 594 comprises an exponential smoothing filter similarto the exponential smoothing filter described above with respect to theclip and smooth filter 566. The output filter is controlled via anoutput filter coefficient module 596. If motion is large, this filter isslowed down, if there is little or no motion, this filter can samplemuch faster and still maintain a clean value. The output from the outputfilter 594 is the pulse of the patient, which is advantageously providedto the display 336.

Alternative to Saturation Transform Module—Bank of Filters

An alternative to the saturation transform of the saturation transformmodule 406 can be implemented with a bank of filters as depicted in FIG.23. As seen in FIG. 23, two banks of filters, a first filter bank 600and a second filter bank 602 are provided. The first filter bank 600receives a first measured signal S_(λb)(t) (the infrared signal samplesin the present embodiment) on a corresponding first filter bank input604, and the second filter bank 602 receives a second measured signalS_(λa)(t) (the red samples in the present embodiment) on a correspondingsecond filter bank input 606. In a preferred embodiment, the first andsecond filter banks utilize static recursive polyphase bandpass filterswith fixed center frequencies and corner frequencies. Recursivepolyphase filters are described in an article Harris, et. al. “DigitalSignal Processing With Efficient Polyphase Recursive All-Pass filters”attached hereto as Appendix A. However, adaptive implementations arealso possible. In the present implementation, the recursive polyphasebandpass filter elements are each designed to include a specific centerfrequency and bandwidth.

There are N filter elements in each filter bank. Each of the filterelements in the first filter bank 600 have a matching (i.e., same centerfrequency and bandwidth) filter element in the second filter bank 602.The center frequencies and the corner frequencies of N elements are eachdesigned to occupy N frequency ranges, 0 to F₁, F₁-F₂, F₂-F₃, F₃-F₄ . .. F_(N-1)-F_(N) as shown in FIG. 23.

It should be understood that the number of filter elements can rangefrom 1 to infinity. However, in the present embodiment, there areapproximately 120 separate filter elements with center frequenciesspread evenly across a frequency range of 25 beats/minute-250beats/minute.

The outputs of the filters contain information about the primary andsecondary signals for the first and second measured signals (red andinfrared in the present example) at the specified frequencies. Theoutputs for each pair of matching filters (one in the first filter bank600 and one in the second filter bank 602) are provided to saturationdetermination modules 610. FIG. 23 depicts only one saturationdetermination module 610 for ease of illustration. However, a saturationdetermination module can be provided for each matched pair of filterelements for parallel processing. Each saturation determination modulehas a ratio module 616 and a saturation equation module 618.

The ratio module 616 forms a ratio of the second output to the firstoutput. For instance, in the present example, a ratio of each red RMSvalue to each corresponding infrared RMS value (Red/IR) is completed inthe ratio module 616. The output of the ratio module 616 provides aninput to the saturation equation module 618 which references acorresponding saturation value for the input ratio.

The output of the saturation equation modules 618 are collected (asrepresented in the histogram module 620) for each of the matched filterpairs. However, the data collected is initially a function of frequencyand saturation. In order to form a saturation transform curve similar tothe curve depicted in FIG. 22, a histogram or the like is generated asin FIG. 24. The horizontal axis represents the saturation value, and thevertical axis represents a summation of the number of points (outputsfrom the saturation equation modules 618) collected at each saturationvalue. In other words, if the output of the saturation equation module618 for ten different matched filter pairs indicates a saturation valueof 98%, then a point in the histogram of FIG. 24 would reflect a valueof 10 at 98% saturation. This results in a curve similar to thesaturation transform curve of FIG. 22. This operation is completed inthe histogram module 620.

The results of the histogram provide a power curve similar to the powercurve of FIG. 22. Accordingly, the arterial saturation can be calculatedfrom the histogram by selecting the peak (greatest number of occurrencesin the area of interest) corresponding to the highest saturation value(e.g., the peak ‘c’ in Figure peaks corresponding to the highestsaturation value peak. Similarly, the venous or background saturationcan be determined from the histogram by selecting the peak correspondingto the lowest saturation value (e.g., the peak ‘d’ in FIG. 24), in amanner similar to the processing in the saturation calculation module408.

It should be understood that as an alternative to the histogram, theoutput saturation (not necessarily a peak in the histogram)corresponding to the highest saturation value could be selected as thearterial saturation with the corresponding ratio representing r_(a).Similarly, the output saturation corresponding to the lowest saturationvalue could be selected as the venous or background saturation with thecorresponding ratio representing r_(v). For example, in this embodiment,the entry ‘a’ in the histogram of FIG. 24 would be chosen as thearterial saturation and the entry in the histogram ‘b’ with the lowestsaturation value would be chosen as the venous or background saturation.

Alternative Determination of Coefficients r_(a) and r_(v)

As explained above, in accordance with the present invention, primaryand secondary signal portions, particularly for pulse oximetry, can bemodeled as follows:

S _(red) =s ₁ +n ₁(red)  (89)

S _(IR) =s ₂ +n ₂(infrared)  (90)

s ₁ =r _(a) s ₂ and n ₁ =r _(v) n ₂  (91)

Substituting Equation (91) into Equation (89) provides the following:

S _(red) =r _(a) s ₂ +r _(v) n ₂(red)  (92)

Note that S_(red) and S_(IR) are used in the model of equations(89)-(92). This is because the discussion below is particularly directedto blood oximetry. S_(red) and S_(IR) correspond to S₁ and S₂ in thepreceding text, and the discussion that follows could be generalized forany measure signal S₁ and S₂.

As explained above, determining r_(a) and r_(v) (which correspond toarterial and venous blood oxygen saturation via a saturation equation)can be accomplished using the saturation transform described above doinga scan of many possible coefficients. Another method to obtain r_(a) andr_(v) based on red and infrared data is to look for r_(a) and r_(v)which minimize the correlation between s_(k) and n_(k), assuming s_(k)is at least somewhat (and preferably substantially) uncorrelated withn_(k) (where k=1 or 2). These values can be found by minimizing thefollowing statistical calculation function for k=2:

$\begin{matrix}{{{Correlation}\left( {s_{2},n_{2}} \right)} = {{\sum\limits_{i}^{\;}{{s_{2}\left( {S_{{red}_{i}},S_{{IR}_{i}},r_{a},r_{v}} \right)}{n_{2}\left( {S_{{red}_{i}},S_{{IR}_{i}},r_{a},r_{v}} \right)}}}}} & (93)\end{matrix}$

where i represents time.

It should be understood that other correlation functions such as anormalized correlation could also be used.

Minimizing this quantity often provides a unique pair of r_(a) and r_(v)if the noise component is uncorrelated to the desired signal component.Minimizing this quantity can be accomplished by solving Equations (90)and (92) for s₂ and n₂, and finding the minimum of the correlation forpossible values of r_(a) and r_(v). Solving for s₂ and n₂ provides thefollowing:

$\begin{pmatrix}S_{red} \\S_{IR}\end{pmatrix} = {\begin{pmatrix}r_{a} & r_{v} \\1 & 1\end{pmatrix}\begin{pmatrix}s_{2} \\n_{2}\end{pmatrix}}$

inverting the two-by-two matrix provides:

Thus,

$\begin{pmatrix}r_{a} & r_{v} \\1 & 1\end{pmatrix}^{- 1} = {\frac{1}{r_{a} - r_{v}}\begin{pmatrix}1 & {- r_{v}} \\{- 1} & r_{a}\end{pmatrix}}$ $\begin{pmatrix}s_{2} \\n_{2}\end{pmatrix} = {\frac{1}{r_{a} - r_{v}}\begin{pmatrix}1 & {- r_{v}} \\{- 1} & r_{a}\end{pmatrix}\begin{pmatrix}s_{red} \\s_{IR}\end{pmatrix}}$ or:$s_{2} = {\frac{1}{r_{a} - r_{v}}\left( {s_{red} - {r_{v}s_{IR}}} \right)}$$n_{2} = {\frac{1}{r_{a} - r_{v}}\left( {{- s_{red}} + {r_{a}s_{IR}}} \right)}$

Preferably, the correlation of equation (93) is enhanced with a userspecified window function as follows:

$\begin{matrix}{{{Correlation}\left( {s_{2},n_{2}} \right)} = {{\sum\limits_{i = 1}^{N\;}{w_{i}{s_{2}\left( {S_{{red}_{i}},S_{{IR}_{i}},r_{a},r_{v}} \right)}{n_{2}\left( {S_{{red}_{i}},S_{{IR}_{i}},r_{a},r_{v}} \right)}}}}} & \left( {93a} \right)\end{matrix}$

The Blackman Window is the presently preferred embodiment. It should beunderstood that there are many additional functions which minimize thecorrelation between signal and noise. The function above is simply one.Thus,

$\begin{matrix}{{{Correlation}\left( {s_{2},n_{2}} \right)} = {{{\sum\limits_{i = 1}^{N\;}\left\lbrack {\frac{w_{i}}{\left( {r_{a} - r_{v}} \right)^{2}}\left( {S_{{red}_{i}} - {r_{v}S_{{IR}_{i}}}} \right)\left( {{- s_{{red}_{i}}} - {r_{a}s_{{IR}_{i}}}} \right)} \right\rbrack}} = {\frac{1}{\left( {r_{a} - r_{v}} \right)^{2}}{{{- {\sum\limits_{i = 1}^{N\;}{\left( s_{{red}_{i}} \right)^{2}w_{i}}}} + {\left( {r_{a} + r_{v}} \right){\sum\limits_{i = 1}^{N}{s_{{IR}_{i}}s_{{red}_{i}}w_{i}}}} + {\sum\limits_{i = 1}^{N}{\left( s_{{IR}_{i}} \right)^{2}w_{i}}}}}}}} & {93(b)}\end{matrix}$

In order to implement the minimization on a plurality of discrete datapoints, the sum of the squares of the red sample points, the sum of thesquares of the infrared sample points, and the sum of the product of thered times the infrared sample points are first calculated (including thewindow function, w_(i)):

${RR} = {\sum\limits_{I = 1}^{n}{\left( S_{{red}_{i}} \right)^{2}w_{i}}}$${II} = {\sum\limits_{i = 1}^{N}{\left( S_{{IR}_{i}} \right)^{2}w_{i}}}$${IRR} = {\sum\limits_{i = 1}^{N}{\left( S_{IR} \right)\left( S_{{red}_{i}} \right)w_{i}}}$

These values are used in the correlation equation (93b). Thus, thecorrelation equation becomes an equation in terms of two variables,r_(a) and r_(v). To obtain r_(a) and r_(v), an exhaustive scan isexecuted for a good cross-section of possible values for r_(a) and r_(v)(e.g., 20-50 values each corresponding to saturation values ranging from30-105). The minimum of the correlation function is then selected andthe values of r_(a) and r_(v) which resulted in the minimum are chosenas r_(a) and r_(v).

Once r_(a) and r_(v) have been obtained, arterial oxygen saturation andvenous oxygen saturation can be determined by provided r_(a) and r_(v)to a saturation equation, such as the saturation equation 502 of thestatistics module 404 which provides an oxygen saturation valuecorresponding to the ratios r_(a) and r_(v).

In a further implementation to obtain r_(a) and r_(v), the same signalmodel set forth above is again used. In order to determine r_(a) andr_(v) in accordance with this implementation, the energy in the signals₂ is maximized under the constraint that s₂ is uncorrelated with n₂.Again, this implementation is based upon minimizing the correlationbetween s and n and on the signal model of the present invention wherethe signal s relates to the arterial pulse and the signal n is the noise(containing information on the venous blood, as well as motion artifactsand other noise); r_(a) is the ratio (RED/IR) related to arterialsaturation and r_(v) is the ratio (RED/IR) related to venous saturation.Accordingly, in this implementation of the present invention, r_(a) andr_(v) are determined such that the energy of the signal s₂ is maximizedwhere s₂ and n₂ are uncorrelated. The energy of the signal s₂ is givenby the following equation:

$\begin{matrix}\begin{matrix}{{{ENERGY}\left( s_{2} \right)} = {\frac{1}{\left( {r_{a} - r_{v}} \right)^{2}}{\sum\limits_{i = 1}^{N}\left( {s_{red} - {r_{v}s_{IR}}} \right)^{2}}}} \\{= {{\frac{1}{\left( {r_{a} - r_{v}} \right)^{2}}{\sum\limits_{i = 1}^{N}\left( s_{{red}_{i}}^{2} \right)}} - {2r_{v}{\sum\limits_{i = 1}^{N}\left( {s_{{red}_{i}}s_{{IR}_{i}}} \right)}} +}} \\{{r_{v}^{2}{\sum\limits_{i = 1}^{N}\left( s_{{IR}_{i}}^{2} \right)}}} \\{= {\frac{1}{\left( {r_{a} - r_{v}} \right)^{2}}\left\lbrack {R_{1} - {2r_{v}R_{1,2}} + {r_{v}^{2}R_{2}}} \right\rbrack}}\end{matrix} & \begin{matrix}\begin{matrix}\begin{matrix}\begin{matrix}\begin{matrix}\begin{matrix}\begin{matrix}\begin{matrix}\begin{matrix}(94) \\\;\end{matrix} \\(95)\end{matrix} \\\;\end{matrix} \\\;\end{matrix} \\\;\end{matrix} \\\;\end{matrix} \\(96)\end{matrix} \\\;\end{matrix} \\\;\end{matrix}\end{matrix}$

where R₁ is the energy of the red signal, R₂ is the energy of theinfrared signal and R_(1,2) is the correlation between the red andinfrared signals.

The correlation between s₂ and n₂ is given by

$\begin{matrix}\begin{matrix}{{{Correlation}\left( {s_{2},n_{2}} \right)} = {\frac{1}{\left( {r_{a} - r_{v}} \right)^{2}}{\sum\limits_{i = 1}^{N}\left( {S_{{red}_{i}} - {r_{v}S_{{ir}_{i}}}} \right)}}} \\{\left( {{- S_{{red}_{i}}} + {r_{a}S_{{IR}_{i}}}} \right)} \\{= {\frac{1}{\left( {r_{a} - r_{v}} \right)^{2}}\left\lbrack {{- R_{1}} + {\left( {r_{a} + r_{v}} \right)R_{1,2}} - {r_{v}r_{a}R_{2}}} \right\rbrack}}\end{matrix} & (97)\end{matrix}$

As explained above, the constraint is that s_(k) and n_(k) (k=2 for thepresent example) are uncorrelated. This “decorrelation constraint” isobtained by setting the correlation of Equation (97) to zero as follows:

−R ₁+(r _(a) +r _(v))R ₁₂ −r _(a) r _(v) R ₂=0  (98)

In other words, the goal is to maximize equation (94) under theconstraint of equation (98).

In order to obtain the goal, a cost function is defined (e.g., aLagrangian optimization in the present embodiment) as follows:

$\begin{matrix}{{J\left( {r_{a},r_{v},\mu} \right)} = {\frac{1}{\left( {r_{a} - r_{v}} \right)^{2}}\left\lbrack {R_{1} - {2r_{v}R_{1,2}} + {r_{v}^{2}R_{2}} + {\mu \left( {{- R_{1}} + {\left( {r_{a} + r_{v}} \right)R_{1,2}} - {r_{a}r_{v\;}R_{2}}} \right)}} \right\rbrack}} & (99)\end{matrix}$

where μ is the Lagrange multiplier. Finding the value of r_(a), r_(v)and μ that solve the cost function can be accomplished using aconstrained optimization method such as described in Luenberger, Linear& Nonlinear Programming, Addison-Wesley, 2d Ed., 1984. Along the samelines, if we assume that the red and infrared signals S_(red) and S_(IR)are non-static, the functions R₁, R₂ and R₁₂ defined above are timedependent. Accordingly, with two equations, two unknowns can be obtainedby expressing the decorrelation constraint set forth in equation (98) attwo different times. The decorrelation constraint can be expressed attwo different times, t₁ and t₂, as follows:

−R ₁(t ₁)+(r _(a) +r _(v))R ₁₂(t ₁)−r _(a) r _(v) R ₂(t ₁)=0  (100)

−R ₁(t ₂)+(r _(a) +r _(v))R ₁₂(t ₂)−r _(a) r _(v) R ₂(t ₂)=0  (101)

Because equations (100) and (101) are non-linear in r_(a) and r_(v), achange of variables allows the use of linear techniques to solve thesetwo equations. Accordingly, with x=r_(a)+r_(v); y=r_(a)r_(v) equations(100) and (101) become

R ₁₂(t ₁)x−R ₂(t ₁)y=R ₁(t ₁)  (102)

R ₁₂(t ₂)x−R ₂(t ₂)y=R ₁(t ₂)  (103)

These equation (102) and (103) can be solved for x and y. Then, solvingfor r_(a) and r_(v) from the changes of variables equations provides thefollowing:

$\begin{matrix}{{r_{v} + \frac{y}{r_{v}}} = {x = {{\succ {r_{v}^{2} - {xr}_{v} + y}} = 0}}} & (104)\end{matrix}$

Solving equation (104) results in two values for r_(v). In the presentembodiment, the r_(v) value that results in x²−r_(v)y>0 is selected. Ifboth values of r_(v) result in x²−r_(v)y>0, the r_(v) that maximizes theenergy of s₂ (Energy(s₂)) at t₂ is selected. r_(v) is then substitutedinto the equations above to obtain r_(a). Alternatively r_(a) can befound directly in the same manner r_(v) was determined.

Alternative to Saturation Transform—Complex FFT

The blood oxygen saturation, pulse rate and a clean plethysmographicwaveform of a patient can also be obtained using the signal model of thepresent invention using a complex FFT, as explained further withreference to FIGS. 25A-25C. In general, by utilizing the signal model ofequations (89)-(92) with two measured signals, each with a first portionand a second portion, where the first portion represents a desiredportion of the signal and the second portion represents the undesiredportion of the signal, and where the measured signals can be correlatedwith coefficients r_(a) and r_(v), a fast saturation transform on adiscrete basis can be used on the sample points from the output of thedecimation operation 402.

FIG. 25A corresponds generally to FIG. 14, with the fast saturationtransform replacing the previously described saturation transform. Inother words, the operations of FIG. 25A can replace the operations ofFIG. 14. As depicted in FIG. 25A, the fast saturation transform isrepresented in a fast saturation transform/pulse rate calculation module630. As in FIG. 14, the outputs are arterial oxygen saturation, a cleanplethysmographic waveform, and pulse rate. FIGS. 25B and 25C illustrateadditional detail regarding the fast saturation transform/pulse ratecalculation module 630. As depicted in FIG. 25B, the fast saturationtransform module 630 has infrared log and red log modules 640, 642 toperform a log normalization as in the infrared and red log modules 480,482 of FIG. 17. Similarly, there are infrared DC removal and red DCremoval modules 644, 646. In addition, there are infrared and redhigh-pass filter modules 645, 647, window function modules 648, 640,complex FFT modules 652, 654, select modules 653, 655, magnitude modules656, 658, threshold modules 660, 662, a point-by-point ratio module 670,a saturation equation module 672, and a select saturation module 680.There are also phase modules 690, 692, a phase difference module 694,and a phase threshold module 696. The output of the select saturationmodule 680 provides the arterial saturation on an arterial saturationoutput line 682.

In this alternative embodiment, the snapshot for red and infraredsignals is 562 samples from the decimation module 402. The infrared DCremoval module 644 and the red DC removal module 646 are slightlydifferent from the infrared and red DC removal modules 484, 486 of FIG.17. In the infrared and red DC removal modules 644, 646 of FIG. 25B, themean of all 563 sample points for each respective channel is calculated.This mean is then removed from each individual sample point in therespective snapshot in order to remove the baseline DC from each sample.The outputs of the infrared and red DC removal modules 644, 646 provideinputs to respective infrared high-pass filter module 645 and redhigh-pass filter module 647.

The high-pass filter modules 645, 647 comprise FIR filters with 51 tapsfor coefficients. Preferably, the high-pass filters comprise Chebychevfilters with a side-lobe level parameter of 30 and a corner frequency of0.5 Hz (i.e., 30 beats/minute). It will be understood that this filtercould be varied for performance. With 562 sample points entering thehigh-pass filters, and with 51 taps for coefficients, there are 512samples provided from these respective infrared and red snapshots at theoutput of the high-pass filter modules. The output of the high-passfilter modules provides an input to the window function modules 648, 650for each respective channel.

The window function modules 648, 650 perform a conventional windowingfunction. A Kaiser windowing function is used in the present embodiment.The functions throughout FIG. 25B maintain a point-by-point analysis. Inthe present embodiment, the time bandwidth product for the Kaiser windowfunction is 7. The output of the window function modules provides aninput to the respective complex Fast Fourier Transform (FFT) modules652, 654.

The complex FFT modules 652, 654 perform complex FFTs on respectiveinfrared and red channels on the data snapshots. The data from thecomplex FFTs is then analyzed in two paths, once which examines themagnitude and one which examines the phase from the complex FFT datapoints. However, prior to further processing, the data is provided torespective infrared and red select modules 653, 655 because the outputof the FFT operation will provide repetitive information from 0-½ thesampling rate and from ½ the sampling rate to the sampling rate. Theselect modules select only samples from 0-½ the sampling rate (e.g.,0-31.25 Hz in the present embodiment) and then select from those samplesto cover a frequency range of the heart rate and one or more harmonicsof the heart rate. In the present embodiment, samples which fall in thefrequency range of 20 beats per minute to 500 beats per minute areselected. This value can be varied in order to obtain harmonics of theheart rate as desired. Accordingly, the output of the select modulesresults in less than 256 samples. In the present embodiment, the samplepoints 2-68 of the outputs of the FFTs are utilized for furtherprocessing.

In the first path of processing, the output from the select modules 653,655 are provided to respective infrared and red magnitude modules 656,658. The magnitude modules 656, 658 perform a magnitude function whereinthe magnitude on a point-by-point basis of the complex FFT points isselected for each of the respective channels. The outputs of themagnitude modules 656, 658 provide an input to infrared and redthreshold modules 660, 662.

The threshold modules 660, 662 examine the sample points, on apoint-by-point basis, to select those points where the magnitude of anindividual point is above a particular threshold which is set at apercentage of the maximum magnitude detected among all the remainingpoints in the snapshots. In the present embodiment, the percentage forthe threshold operation is selected as 1% of the maximum magnitude.

After thresholding, the data points are forwarded to a point-by-pointratio module 670. The point-by-point ratio module takes the red overinfrared ratio of the values on a point-by-point basis. However, afurther test is performed to qualify the points for which a ratio istaken. As seen in FIG. 25B, the sample points output from the selectmodules 653, 655 are also provided to infrared and red phase modules690, 692. The phase modules 690, 692 select the phase value from thecomplex FFT points. The output of the phase modules 690, 692 is thenpresented to a phase difference module 694.

The phase difference module 694 calculates the difference in phasebetween the corresponding data points from the phase modules 690, 692.If the magnitude of the phase difference between any two correspondingpoints is less than a particular threshold (e.g., 0.1 radians) in thepresent embodiment), then the sample points qualify. If the phase of twocorresponding sample points is too far apart, then the sample points arenot used. The output of the phase threshold module 696 provides anenable input to the RED/IR rate module 670. Accordingly, in order forthe ratio of a particular pair of sample points to be taken, the threetests are executed:

-   -   1. the red sample must pass the red threshold 660;    -   2. the infrared sample must pass the infrared threshold 662; and    -   3. the phase between the two points must be less than the        predefined threshold as determined in the phase threshold 696.

For those sample points which qualify, a ratio is taken in the ratiomodule 670. For those points which do not qualify, the saturation is setto zero at the output of the saturation equation 672.

The resulting ratios are provided to a saturation equation module whichis the same as the saturation equation modules 502, 520 in thestatistics module 504. In other words, the saturation equation module672 accepts the ratio on a point-by-point basis and provides as anoutput a corresponding saturation value corresponding to the discreteratio points. The saturation points output from the saturation equationmodule 672 provide a series of saturation points which could be plottedas saturation with respect to frequency. The frequency reference wasentered into the points at the complex FFT stage.

The arterial (and the venous) saturation can then be selected, asrepresented in the select arterial saturation module 680, in one of twomethods according to the present invention. According to one method, thearterial saturation value can be selected simply as the pointcorresponding to the largest saturation value for all points output fromthe saturation equation module 672 for a packet. Alternatively, ahistogram similar to the histogram of FIG. 22 can be generated in whichthe number of saturation values at different frequencies (points) aresummed to form a histogram of the number of occurrences for eachparticular saturation value. In either method, the arterial saturationcan be obtained and provided as an output to the select arterialsaturation module on the arterial saturation output line 682. In orderto obtain the venous saturation, the minimum arterial saturation value,of points that exhibit non-zero value, is selected rather than themaximum arterial saturation value. The saturation can be provided to thedisplay 336.

The fast saturation transform information can also be used to providethe pulse rate and the clean plethysmographic wave form as furtherillustrated in FIG. 25C. In order to obtain the pulse rate and a cleanplethysmographic wave form, several additional functions are necessary.As seen in FIG. 25C, the pulse rate and clean plethysmographic wave formare determined using a window function module 700, a spectrum analysismodule 702 and an inverse window function module 704.

As depicted in FIG. 25C, the input to the window function module 700 isobtained from the output of the complex FFT modules 652 or 654. In thepresent embodiment, only one measured signal is necessary. Another inputto the window function module 700 is the arterial saturation obtainedfrom the output of the select arterial saturation module 680.

The window function module performs a windowing function selected topass those frequencies that significantly correlate to the frequencieswhich exhibited saturation values very close to the arterial saturationvalue. In the present embodiment, the following windowing function isselected:

$\begin{matrix}{1 - \left\lbrack \frac{{SAT}_{art} - {SAT}_{n}}{100} \right\rbrack^{15}} & (105)\end{matrix}$

where SAT_(n) equals the saturation value corresponding to eachparticular frequency for the sample points and SAT_(art) represents thearterial saturation as chosen at the output of the select arterialsaturation module 680. This window function is applied to the windowfunction input representing the complex FFT of either the red or theinfrared signal. The output of the window function module 700 is a redor infrared signal represented with a frequency spectrum as determinedby the FFT, with motion artifacts removed by the windowing function. Itshould be understood that many possible window functions can beprovided. In addition, with the window function described above, itshould be understood that using a higher power will provide more noisesuppression.

In order to obtain pulse rate, the output points from the windowfunction module 700 are provided to a spectrum analysis module 702. Thespectrum analysis module 702 is the same as the spectrum analysis module590 of FIG. 20. In other words, the spectrum analysis module 702determines the pulse rate by determining the first harmonic in thefrequency spectrum represented by the output points of the windowingfunction 700. The output of spectrum analysis module 702 is the pulserate.

In order to obtain a clean plethysmographic waveform, the output of thewindowing function 700 is applied to an inverse window function module704. The inverse window function module 704 completes an inverse of theKaiser window function of the window function module 648 or 650 of FIG.25B. In other words, the inverse window function 704 does apoint-by-point inverse of the Kaiser function for points that are stilldefined. The output is a clean plethysmographic waveform.

Accordingly, by using a complex FFT and windowing functions, the noisecan be suppressed from the plethysmographic waveform in order to obtainthe arterial saturation, the pulse rate, and a clean plethysmographicwaveform. It should be understood that although the above descriptionrelates to operations primarily in the frequency domain, operations thatobtain similar results could also be accomplished in the time domain.

Relation to Generalized Equations

The measurements described for pulse oximetry above are now related backto the more generalized discussion above. The signals (logarithmconverted) transmitted through the finger 310 at each wavelength λa andλb are:

S _(λa)(t)=S _(λred1)(t)=ε_(HbO2,λa) c ^(A) _(HbO2) x ^(A)(t)+ε_(Hb,λa)c ^(A) _(Hb) x ^(A)(t)+ε_(HbO2,λa) c ^(V) _(HbO2) x ^(V)(t)+ε_(Hb,λa) c^(V) _(Hb) x ^(V)(t)+n _(λa)(t);  (105a)

S _(λa)(t)=ε_(HbO2,λa) c ^(A) _(HbO2) x ^(A)(t)+ε_(Hb,λa) c ^(A) _(Hb) x^(A)(t)+n _(λa)(t);  (105b)

S _(λa)(t)=x _(λa)(t)+n _(λa)(t);  (105c)

S _(λb)(t)=S _(λred2)(t)=ε_(HbO2,λb) c ^(A) _(HbO2) x ^(A)(t)+ε_(Hb,λb)c ^(A) _(Hb) x ^(A)(t)+ε_(HbO2,λb) c ^(V) _(HbO2) x ^(V)(t)+ε_(Hb,λb) c^(V) _(Hb) x ^(V)(t)+n _(λb)(t)  (106a)

S _(λb)(t)=ε_(HbO2,λb) c ^(A) _(HbO2) x ^(A)(t)+ε_(Hb,λb) c ^(A) _(Hb) x^(A)(t)+n _(λb)(t)  (106b)

S _(λb)(t)=s _(λb)(t)+n _(λb)(t)  (106c)

The variables above are best understood as correlated to FIG. 6 c asfollows: assume the layer in FIG. 6 c containing A₃ and A₄ representsvenous blood in the test medium, with A₃ representing deoxygenatedhemoglobin (Hb) and A₄ representing oxygenated hemoglobin (HBO2) in thevenous blood. Similarly, assume that the layer in FIG. 6 c containing A₅and A₆ represents arterial blood in the test medium, with A₅representing deoxygenated hemoglobin (Hb) and A₆ representing oxygenatedhemoglobin (HBO2) in the arterial blood. Accordingly, c^(V)HbO2represents the concentration of oxygenated hemoglobin in the venousblood, c^(V)Hb represents the concentration of deoxygenated hemoglobinin the venous blood, x^(V) represents the thickness of the venous blood(e.g., the thickness the layer containing A₃ and A₄). Similarly,c^(A)HbO2 represents the concentration of oxygenated hemoglobin in thearterial blood, c^(A)Hb represents the concentration of deoxygenatedhemoglobin in the arterial blood, and x^(A) represents the thickness ofthe arterial blood (e.g., the thickness of the layer containing A₅ andA₆)

The wavelengths chosen are typically one in the visible red range, i.e.,λa, and one in the infrared range, i.e., λb. Typical wavelength valueschosen are λa=660 nm and λb=910 nm. In accordance with the constantsaturation method, it is assumed that c^(A) _(Hb02)(t)/c^(A)_(Hb)(t)=constant₁ and c^(V) _(Hb02)(t)/c^(V) _(Hb)(t)=constant₂. Theoxygen saturation of arterial and venous blood changes slowly, if atall, with respect to the sample rate, making this a valid assumption.The proportionality coefficients for equations (105) and (106) can thenbe written as:

$\begin{matrix}{{r_{a}(t)} = {\frac{\in_{{{Hb}\; 02},{\lambda \; a}}{{c_{{Hb}\; 02}^{A}{x(t)}} +} \in_{{Hb},{\lambda \; a}}{c_{Hb}{x(t)}}}{\in_{{{Hb}\; 02},{\lambda \; b}}{{c_{{Hb}\; 02}^{A}{x(t)}} +} \in_{{Hb},{\lambda \; b}}{C_{Hb}^{A}{x(t)}}}*}} & (107) \\{{s_{\lambda \; a}(t)} = {{r_{a}(t)}{s_{\lambda \; b}(t)}}} & \left( {108a} \right)\end{matrix}$n _(λa)(t)≠r _(a)(t)n _(λb)(t)  (109a)

n _(λa)(t)=r _(v)(t)n _(λb)(t)  (108b)

s _(λa)(t)≠r _(v)(t)s _(λb)(t)  (109b)

In pulse oximetry, it is typically the case that both equations (108)and (109) can be satisfied simultaneously.

Multiplying equation (106) by r_(a)(t) and then subtracting equation(106) from equation (105), a non-zero secondary reference signal n′(t)is determined by:

$\begin{matrix}\begin{matrix}{{n^{\prime}(t)} = {{S_{\lambda \; a}(t)} - {{r_{a}(t)}{S_{\lambda \; b}(t)}}}} \\{= {{ɛ_{{{Hb}\; O\; 2},{\lambda \; a}}c_{{Hb}\; O\; 2}^{V}{x^{V}(t)}} + {ɛ_{{Hb},{\lambda \; a}}c_{Hb}^{V}{x^{V}(t)}} + {n_{\lambda \; a}(t)} -}} \\{{{r_{a}(t)}\left\lbrack {{ɛ_{{{Hb}\; O\; 2},{\lambda \; b}}c_{{HbO}\; 2}^{V}{x^{V}(t)}} + {ɛ_{{Hb},{\lambda \; b}}c_{Hb}^{V}{x^{V}(t)}} + {n_{\lambda \; b}(t)}} \right\rbrack}}\end{matrix} & \begin{matrix}\begin{matrix}\left( {110a} \right) \\\;\end{matrix} \\\left( {111a} \right)\end{matrix}\end{matrix}$

Multiplying equation (106) by r_(v)(t) and then subtracting equation(106) from equation (105), a non-zero primary reference signal s′(t) isdetermined by:

$\begin{matrix}\begin{matrix}{{{s’}(t)} = {{S_{\lambda \; a}(t)} - {{r_{v\;}(t)}{S_{\lambda \; b}(t)}}}} \\{= {{s_{\lambda \; a}(t)} - {{r_{v}(t)}{s_{\lambda \; b}(t)}}}}\end{matrix} & \begin{matrix}\left( {110b} \right) \\\left( {111b} \right)\end{matrix}\end{matrix}$

The constant saturation assumption does not cause the venouscontribution to the absorption to be canceled along with the primarysignal portions s_(λa)(t) and s_(λb)(t). Thus, frequencies associatedwith both the low frequency modulated absorption due to venousabsorption when the patient is still and the modulated absorption due tovenous absorption when the patient is moving are represented in thesecondary reference signal n′(t). Thus, the correlation canceler orother methods described above remove or derive both erraticallymodulated absorption due to venous blood in the finger under motion andthe constant low frequency cyclic absorption of venous blood.

To illustrate the operation of the oximeter of FIG. 11 to obtain cleanwaveform, FIGS. 26 and 27 depict signals measured for input to areference processor of the present invention which employs the constantsaturation method, i.e., the signals S_(λa)(t)=S_(λred)(t) andS_(λb)(t)=S_(λIR)(t). A first segment 26 a and 27 a of each of thesignals is relatively undisturbed by motion artifact, i.e., the patientdid not move substantially during the time period in which thesesegments were measured. These segments 26 a and 27 a are thus generallyrepresentative of the primary plethysmographic waveform at each of themeasured wavelengths. A second segment 26 b and 27 b of each of thesignals is affected by motion artifact, i.e., the patient did moveduring the time period in which these segments were measured. Each ofthese segments 26 b and 27 b shows large motion induced excursions inthe measured signal. A third segment 26 c and 27 c of each of thesignals is again relatively unaffected by motion artifact and is thusgenerally representative of the primary plethysmographic waveform ateach of the measured wavelengths.

FIG. 28 shows the secondary reference signaln′(t)=n_(λa)(t)−r_(a)n_(λb)(t), as determined by a reference processorof the present invention. Again, the secondary reference signal n′(t) iscorrelated to the secondary signal portions n_(λa) and n_(λb). Thus, afirst segment 28 a of the secondary reference signal n′(t) is generallyflat, corresponding to the fact that there is very little motion inducednoise in the first segments 26 a and 27 a of each signal. A secondsegment 28 b of the secondary reference signal n′(t) exhibits largeexcursions, corresponding to the large motion induced excursions in eachof the measured signals. A third segment 28 c of the noise referencesignal n′(t) is generally flat, again corresponding to the lack ofmotion artifact in the third segments 26 c and 27 c of each measuredsignal.

It should also be understood that a reference processor could beutilized in order to obtain the primary reference signals′(t)=s_(λa)−r_(v)s_(λb)(t). The primary reference signal s′(t) would begenerally indicative of the plethysmograph waveform.

FIGS. 29 and 30 show the approximations s″_(λa)(t) and s″_(λb)(t) to theprimary signals s_(λa)(t) and s_(λb)(t) as estimated by a correlationcanceler using a secondary reference signal n′(t). Note that the scaleof FIGS. 26 through 30 is not the same for each figure to betterillustrate changes in each signal. FIGS. 29 and 30 illustrate the effectof correlation cancellation using the secondary reference signal n′(t)as determined by the reference processor. Segments 29 b and 30 b are notdominated by motion induced noise as were segments 26 b and 27 b of themeasured signals. Additionally, segments 29 a, 30 a, 29 c, and 30 c havenot been substantially changed from the measured signal segments 26 a,27 a, 26 c, and 27 c where there was no motion induced noise.

It should be understood that approximation n″_(λa)(t) and n″_(λb)(t) tothe secondary signals n_(λa)(t) and n_(λb)(t) as estimated by acorrelation canceler using a primary reference signal s′(t) can also bedetermined in accordance with the present invention.

Method for Estimating Primary and Secondary Signal Portions of MeasuredSignals in a Pulse Oximeter

Implementing the various embodiments of the correlation cancelerdescribed above in software is relatively straightforward given theequations set forth above, and the detailed description above. However,a copy of a computer program subroutine, written in the C programminglanguage, which calculates a primary reference s′(t) using the constantsaturation method and, using a joint process estimator 572 whichimplements a joint process estimator using the equations (54)-(64) isset forth in Appendix B. This joint process estimator estimates a goodapproximation to the primary signal portions of two measured signals,each having a primary portion which is correlated to the primaryreference signal s′(t) and a secondary portion which is correlated tothe secondary reference signal n′(t). This subroutine is another way toimplement the steps illustrated in the flowchart of FIG. 9 for a monitorparticularly adapted for pulse oximetry. The two signals are measured attwo different wavelengths λa and λb, where λa is typically in thevisible region and λb is typically in the infrared region. For example,in one embodiment of the present invention, tailored specifically toperform pulse oximetry using the constant saturation method, λa=660 nmand λb=940 nm.

The correspondence of the program variables to the variables defined inequations (54)-(64) in the discussion of the joint process estimator isas follows:

-   -   Δ_(m)(t)=nc[m]·Delta    -   Γ_(f,m)(t)=nc[m]·fref    -   Γ_(b,m)(t)=nc[m]·bref    -   f_(m)(t)=nc[m]·ferr    -   b_(m)(t)=nc[m]·berr    -   ℑ_(m)(t)=nc[m]·Fswsqr    -   β_(m)(t)=nc[m]·Bswsqr    -   γ_(m)(t)=nc[m]·Gamma    -   ρ_(m,λa)(t)=nc[m]·Roh_a    -   ρ_(m,λb)(t)=nc[m]·Roh_b    -   e_(m,λa)(t)=nc[m]·err_a    -   e_(m,λb)(t)=nc[m]·err_b    -   κ_(m,λa)(t)=nc[m]·K_a    -   κ_(m,λb)(t)=nc[m]·K_b

A first portion of the program performs the initialization of theregisters 90, 92, 96, and 98 and intermediate variable values as in the“INITIALIZED CORRELATION CANCELER” action block 120. A second portion ofthe program performs the time updates of the delay element variables 110with the value at the input of each delay element variable 110 is storedin the delay element variable 110 as in the “TIME UPDATE OF LEFT [Z⁻¹]ELEMENTS” action block 130. The calculation of saturation is performedin a separate module. Various methods for calculation of the oxygensaturation are known to those skilled in the art. One such calculationis described in the articles by G. A. Mook, et al, and Michael R. Neumancited above. Once the concentration of oxygenated hemoglobin anddeoxygenated hemoglobin are determined, the value of the saturation isdetermined similarly to equations (72) through (79) wherein measurementsat times t₁ and t₂ are made at different, yet proximate times over whichthe saturation is relatively constant. For pulse oximetry, the averagesaturation at time t=(t₁+t₂)/2 is then determined by:

$\begin{matrix}\begin{matrix}{{{Sat}_{arterial}(t)} = \frac{C_{{Hb}\; 02}^{A}(t)}{{C_{{Hb}\; 02}^{A}(t)} + {C_{Hb}^{A}(t)}}} \\{= \frac{\in_{{Hb},{\lambda \; a}}{- {\in_{{Hb},{\lambda \; b}}\left( {\Delta \; {S_{\lambda \; a}/\Delta}\; S_{\lambda \; b}} \right)}}}{\in_{{HB},{\lambda \; a}}{- {\in_{{{Hb}\; 02},{\lambda \; a}}{{- \left( {\in_{{HB},{\lambda \; b}}{- \in_{{{Hb}\; 02},{\lambda b}}}} \right)}\left( {\Delta \; {S_{\lambda \; a}/{\Delta S}_{\lambda \; b}}} \right)}}}}}\end{matrix} & \begin{matrix}\begin{matrix}\left( {112a} \right) \\\;\end{matrix} \\\left( {112b} \right)\end{matrix} \\\begin{matrix}{{{Sat}_{venous}(t)} = \frac{C_{{Hb}\; 02}^{V}(t)}{{C_{{Hb}\; 02}^{V}(t)} + {C_{Hb}^{V}(t)}}} \\{= \frac{\in_{{Hb},{\lambda \; a}}{- {\in_{{Hb},{\lambda \; b}}\left( {\Delta \; {n_{\lambda \; a}/\Delta}\; n_{\lambda \; b}} \right)}}}{\in_{{HB},{\lambda \; a}}{- {\in_{{{Hb}\; 02},{\lambda \; a}}{{- \left( {\in_{{HB},{\lambda \; b}}{- \in_{{{Hb}\; 02},{\lambda b}}}} \right)}\left( {\Delta \; {n_{\lambda \; a}/\Delta}\; n_{\lambda \; b}} \right)}}}}}\end{matrix} & \begin{matrix}\begin{matrix}\left( {113a} \right) \\\;\end{matrix} \\\left( {113b} \right)\end{matrix}\end{matrix}$

A third portion of the subroutine calculates the primary reference orsecondary reference, as in the “CALCULATE PRIMARY OR SECONDARY REFERENCE(s′(t) or n′(t)) FOR TWO MEASURED SIGNAL SAMPLES” action block 140 forthe signals S_(λa)(t) and S_(λb)(t) using the proportionality constantsr_(a)(t) and r_(v)(t) determined by the constant saturation method as inequation (3). The saturation is calculated in a separate subroutine anda value of r_(a)(t) or r_(v)(t) is imported to the present subroutinefor estimating either the primary portions s_(λa)(t) and s_(λb)(t) orthe secondary portions n_(λa)(t) and n_(λb)(t) of the composite measuredsignals S_(λa)(t) and S_(λb)(t).

A fourth portion of the program performs Z-stage update as in the “ZEROSTAGE UPDATE” action block 150 where the Z-stage forward predictionerror F_(o)(t) and Z-stage backward prediction error b_(o)(t) are setequal to the value of the reference signal n′(t) or s′(t) justcalculated. Additionally zero-stage values of intermediate variablesℑ_(o) and β₀(t)(nc[m]·Fswsqr and nc[m]·Bswsqr in the program) arecalculated for use in setting registers 90, 92, 96, and 98 values in theleast-squares lattice predictor 70 in the regression filters 80 a and 80b.

A fifth portion of the program is an iterative loop wherein the loopcounter, M, is reset to zero with a maximum of m=NC_CELLS, as in the“m=0” action block 160 in FIG. 9. NC_CELLS is a predetermined maximumvalue of iterations for the loop. A typical value for NC_CELLS isbetween 6 and 10, for example. The conditions of the loop are set suchthat the loop iterates a minimum of five times and continues to iterateuntil a test for conversion is met or m−NC_CELLS. The test forconversion is whether or not the sum of the weighted sum of fourprediction errors plus the weighted sum of backward prediction errors isless than a small number, typically 0.00001 (i.e.,ℑ_(m)(t)+βm(t)≦0.00001).

A sixth portion of the program calculates the forward and backwardreflection coefficient Γ_(m,f)(t) and Γ_(m,b)(t) register 90 and 92values (nc[m]·fref and nc[m]·bref in the program) as in the “ORDERUPDATE m^(th)-STAGE OF LSL-PREDICTOR” action block 170. Then forward andbackward prediction errors f_(m)(t) and b_(m)(t) (nc[m]·ferr andnc[m]·berr in the program) are calculated. Additionally, intermediatevariables ℑ_(m)(t), βm(t), and γ(t) (nc[m]·Fswsqr, nc[m]·Bswsqr,nc[m]·gamma in the program) are calculated. The first cycle of the loopuses the value for nc[0]·Fswsqr and nc[0]·Bswsqr calculated in the ZEROSTAGE UPDATE portion of the program.

A seventh portion of the program, still within the loop begun in thefifth portion of the program, calculates the regression coefficientregister 96 and 98 values κ_(m,λa)(t) and κ_(m,λb)(t) (nc[m]·K_a andnc[m]·K_b in the program) in both regression filters, as in the “ORDERUPDATE m^(th) STAGE OF REGRESSION FILTER(S)” action block 180.Intermediate error signals and variables e_(m,λa)(t), e_(m,λb)(t),ρ_(m,λa)(t), and ρ_(m,λb)(t) (nc[m]·err_a and nc[m]·err_b, nc[m]·roh_a,and nc[m]·roh_b in the subroutine) are also calculated.

The loop iterates until the test for convergence is passed. The test forconvergence of the joint process estimator is performed each time theloop iterates analogously to the “DONE” action block 190. If the sum ofthe weighted sums of the forward and backward prediction errorsℑ_(m)(t)+βm(t) is less than or equal to 0.00001, the loop terminates.Otherwise, sixth and seventh portions of the program repeat.

The output of the present subroutine is a good approximation to theprimary signals s″_(λa)(t) and s″_(λb)(t) or the secondary signalsn″_(λa)(t) and n″_(λb)(t) for the set of samples S_(λa)(t) and S_(λb)(t)input to the program. After approximations to the primary signalportions or the secondary signals portions of many sets of measuredsignal samples are estimated by the joint process estimator, acompilation of the outputs provides waves which are good approximationsto the plethysmographic wave or motion artifact at each wavelength, λaand λb.

It should be understood that the subroutine of Appendix B is merely oneembodiment which implements the equations (54)-(64). Althoughimplementation of the normalized and QRD-LSL equations is alsostraightforward, a subroutine for the normalized equations is attachedas Appendix C, and a subroutine for the QRD-LSL algorithm is attached asAppendix D.

While one embodiment of a physiological monitor incorporating aprocessor of the present invention for determining a reference signalfor use in a correlation canceler, such as an adaptive noise canceler,to remove or derive primary and secondary components from aphysiological measurement has been described in the form of a pulseoximeter, it will be obvious to one skilled in the art that other typesof physiological monitors may also employ the above describedtechniques.

Furthermore, the signal processing techniques described in the presentinvention may be used to compute the arterial and venous blood oxygensaturations of a physiological system on a continuous or nearlycontinuous time basis. These calculations may be performed, regardlessof whether or not the physiological system undergoes voluntary motion.

Furthermore, it will be understood that transformations of measuredsignals other than logarithmic conversion and determination of aproportionality factor which allows removal or derivation of the primaryor secondary signal portions for determination of a reference signal arepossible. Additionally, although the proportionality factor r has beendescribed herein as a ratio of a portion of a first signal to a portionof a second signal, a similar proportionality constant determined as aratio of a portion of a second signal to a portion of a first signalcould equally well be utilized in the processor of the presentinvention. In the latter case, a secondary reference signal wouldgenerally resemble n′(t)=n_(λb)(t)−rn_(λa)(t).

Furthermore, it will be understood that correlation cancellationtechniques other than joint process estimation may be used together withthe reference signals of the present invention. These may include butare not limited to least mean square algorithms, wavelet transforms,spectral estimation techniques, neural networks, Weiner and Kalmanfilters among others.

One skilled in the art will realize that many different types ofphysiological monitors may employ the teachings of the presentinvention. Other types of physiological monitors include, but are in notlimited to, electro cardiographs, blood pressure monitors, bloodconstituent monitors (other than oxygen saturation) monitors,capnographs, heart rate monitors, respiration monitors, or depth ofanesthesia monitors. Additionally, monitors which measure the pressureand quantity of a substance within the body such as a breathalizer, adrug monitor, a cholesterol monitor, a glucose monitor, a carbon dioxidemonitor, a glucose monitor, or a carbon monoxide monitor may also employthe above described techniques.

Furthermore, one skilled in the art will realize that the abovedescribed techniques of primary or secondary signal removal orderivation from a composite signal including both primary and secondarycomponents can also be performed on electrocardiography (ECG) signalswhich are derived from positions on the body which are close and highlycorrelated to each other. It should be understood that a tripolarLaplacian electrode sensor such as that depicted in FIG. 31 which is amodification of a bipolar Laplacian electrode sensor discussed in thearticle “Body Surface Laplacian ECG Mapping” by Bin He and Richard J.Cohen contained in the journal IEEE Transactions on BiomedicalEngineering, Vol. 39, No. 11, November 1992 could be used as an ECGsensor. It must also be understood that there are a myriad of possibleECG sensor geometry's that may be used to satisfy the requirements ofthe present invention. The same type of sensor could also be used forEEG and EMG measurements.

Furthermore, one skilled in the art will realize that the abovedescribed techniques can also be performed on signals made up ofreflected energy, rather than transmitted energy. One skilled in the artwill also realize that a primary or secondary portion of a measuredsignal of any type of energy, including but not limited to sound energy,X-ray energy, gamma ray energy, or light energy can be estimated by thetechniques described above. Thus, one skilled in the art will realizethat the techniques of the present invention can be applied in suchmonitors as those using ultrasound where a signal is transmitted througha portion of the body and reflected back from within the body backthrough this portion of the body. Additionally, monitors such as echocardiographs may also utilize the techniques of the present inventionsince they too rely on transmission and reflection.

While the present invention has been described in terms of aphysiological monitor, one skilled in the art will realize that thesignal processing techniques of the present invention can be applied inmany areas, including but not limited to the processing of aphysiological signal. The present invention may be applied in anysituation where a signal processor comprising a detector receives afirst signal which includes a first primary signal portion and a firstsecondary signal portion and a second signal which includes a secondprimary signal portion and a second secondary signal portion. Thus, thesignal processor of the present invention is readily applicable tonumerous signal processing areas.

1. In a signal processor, a method of determining a measurement of acharacteristic of arterial blood, the method comprising: transformingfirst and second time-domain signals into respective first and secondfrequency-domain signals, the first and second time-domain signals beingindicative of light that has been attenuated by body tissue carryingarterial blood; determining one or more values for a plurality ofnon-zero frequency components of the first and second frequency-domainsignals that are indicative of the strength of one or more frequencycomponents of the first frequency-domain signal versus the strength ofone or more corresponding frequency components in the secondfrequency-domain signal; selecting one or more frequency components thatexhibit physiological characteristics of arterial blood using, at leastin part, the corresponding one or more values; and determining themeasurement for the characteristic of arterial blood using the selectedone or more frequency components.
 2. The method of claim 1, wherein thecharacteristic of arterial blood comprises the oxygen saturationthereof.
 3. The method of claim 2, wherein selecting one or morefrequency components that exhibit physiological characteristics ofarterial blood comprises calculating a plurality of possible oxygensaturation values.
 4. The method of claim 3, wherein selecting one ormore frequency components that exhibit physiological characteristics ofarterial blood further comprises analyzing a histogram of the pluralityof possible oxygen saturation values.
 5. The method of claim 1, whereinthe plurality of non-zero frequency components span a range offrequencies that includes one or more harmonics of the pulse rate of thepulsing blood.
 6. The method of claim 1, wherein each value comprises aratio of the strength of one or more frequency components in the firstfrequency-domain signal to the strength of the corresponding one or morefrequency components in the second frequency-domain signal.
 7. Themethod of claim 6, wherein the first and second frequency-domain signalsrespectively comprise first and second Fourier-transformed signals. 8.The method of claim 7, wherein the strength of the one or more frequencycomponents in the first and second Fourier-transformed signalsrespectively comprises the magnitude of the first and secondFourier-transformed transform signals for the one or more frequencycomponents.
 9. A signal processor apparatus for determining ameasurement value for a characteristic of arterial blood, the signalprocessor apparatus comprising: a processor programmed to perform amethod comprising, transforming first and second time-domain signalsinto respective first and second frequency-domain signals, the first andsecond time-domain signals being indicative of light that has beenattenuated by body tissue carrying arterial blood; determining one ormore values for a plurality of non-zero frequency components of thefirst and second frequency-domain signals that are indicative of thestrength of one or more frequency components of the firstfrequency-domain signal versus the strength of one or more correspondingfrequency components in the second frequency-domain signal; selectingone or more frequency components that exhibit physiologicalcharacteristics of arterial blood using, at least in part, thecorresponding one or more values; and determining the measurement forthe characteristic of arterial blood using the selected one or morefrequency components.
 10. The signal processor apparatus of claim 9,wherein the characteristic of arterial blood comprises the oxygensaturation thereof.
 11. The signal processor apparatus of claim 10,wherein selecting one or more frequency components that exhibitphysiological characteristics of arterial blood comprises calculating aplurality of possible oxygen saturation values.
 12. The signal processorapparatus of claim 11, wherein selecting one or more frequencycomponents that exhibit physiological characteristics of arterial bloodfurther comprises analyzing a histogram of the plurality of possibleoxygen saturation values.
 13. The signal processor apparatus of claim 9,wherein the plurality of non-zero frequency components span a range offrequencies that includes one or more harmonics of the pulse rate of thepulsing blood.
 14. The signal processor apparatus of claim 9, whereineach value comprises a ratio of the strength of one or more frequencycomponents in the first frequency-domain signal to the strength of thecorresponding one or more frequency components in the secondfrequency-domain signal.
 15. The signal processor apparatus of claim 14,wherein the first and second frequency-domain signals respectivelycomprise first and second Fourier-transformed signals.
 16. The signalprocessor apparatus of claim 15, wherein the strength of the one or morefrequency components in the first and second Fourier-transformed signalsrespectively comprises the magnitude of the first and secondFourier-transformed transform signals for the one or more frequencycomponents.